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Masters of Medicine 

Title Author 

JOHN HUNTER .... Stephen Paget 

WILLIAM HARVEY . . . 'Tf Arcy Power 


WILLIAM STOKES . . . Sir William Stokes 

SIR BENJAMIN BRODIE . . Timothy Holmes 

CLAUDE BERNARD . . . Sir Michael Foster 

HERMANN L. F. VON HELMHOLTZ, y. G. M i Kendrick 

In Preparation 

THOMAS SYDENHAM . . y. F. Payne 
ANDREAS VESALIUS . . . C. Louis Taylor 





n E D I C I N E 

Hermann Ludwig 
Ferdinand von Helmholtz 


I * 

M.D., LL.D., F.R.SS.L. AND E. 








Copyright by T. Fisher Vnwin, 1899, for Great Britain 

and Longmans, Green W Co. for the 

United States of America 







THIS work is a record of the achievements in 
scientific discovery and invention of one of 
the greatest minds of the nineteenth century. 
Helmholtz was one whose private life was 
known only to a few, and he would have 
instinctively recoiled from biographical revela- 
tions of a purely personal character. At the 
same time, I have endeavoured to give the 
reader some idea of the man calm, placid, 
reserved, thoughtful whose love of truth, 
yearning spirit of inquiry, and great intel- 
lectual powers give him a place in the front 
ranks of the interpreters of Nature. A life 
full of intellectual activity, creative, ever pro- 
ductive, could not contain much in the way 
of trivial incident. I have also tried, by 
following a historical method, to trace the 
history of any branch of inquiry up to the 


point when it came under the survey of 
Helmholtz, and then I have given an account 
of the contributions made by himself. Few 
are able to tread in the footsteps of Helm- 
holtz, even although these are carefully pointed 
out by a competent guide; but this volume 
may at all events give an outline of the paths 
along which he trod. 

The proofs have been read by Mr J. L. 
Galbraith, of the Library of the University of 
Glasgow, to whom I owe my thanks; and I 
have gratefully to acknowledge much valu- 
able assistance and friendly criticism from Dr 
Cargill G. Knott, Lecturer on Mathematical 
Physics in the University of Edinburgh. 

The characteristic portrait was most kindly 
lent by Lord Kelvin. It was taken by Mr 
Henderson, a student of physics at that time, 
and it represents Helmholtz at his lecture table 
on July 7, 1894, a few days before his final 


September, 1899. 




CENTURIES . . . . .18 


ANIMAL HEAT . . . .25 





THALMOSCOPE . . . . .71 


















HOLTZ 250 






INDEX ....... 295 

Hermann von Helmholtz 



VON HELMHOLTZ was born on August 
3ist, 1821, at Potsdam, near Berlin. He was the son 
of Ferdinand Helmholtz, a teacher of philology and 
philosophy in the Gymnasium, a man of high culture 
and of great general intelligence, who was much 
respected for the thorough way in which he per- 
formed the duties of his position, and for the integrity 
of his character. His mother was the daughter of a 
Hanoverian artillery officer of the name of Penne, 
a lineal descendant of William Penn, the great Quaker 
who founded Pennsylvania ; while the grandmother, on 
his mother's side, sprang from a family of French 
refugees, of the name of Sauvage. Thus Helmholtz 
had German, English and French blood in his veins. 
We are free to speculate as to the origin of his great 


talents, and as to his dignified presence in mature years. 
It is possible that something of his calm, reserved, self- 
possessed manner may have come through the maternal 
line from the old Quaker statesman who made his mark 
on the new world. There is no trace of any hereditary 
aptitude for mathematics, and it must be said that the 
atmosphere of his father's home was not favourable 
to the development of any latent faculties in that 

The little we know of his early life was revealed 
by Helmholtz himself in a speech delivered in 1891, 
in reply to the toast of his health at a banquet given 
in honour of his seventieth birthday. For the first 
seven years of his life he was a weakly boy, confined 
for long periods to his room, and frequently to his bed ; 
but he was fond of such amusements as were possible, 
and he showed great activity of mind. His parents 
gave him much of their time and attention. Picture 
books amused him, and at an early age he read widely. 
A collection of wooden blocks he specially mentioned 
as a favourite plaything, and while he wiled away the 
time with these blocks, he formed from them some 
geometric conceptions that were the first indications 
of mathematical genius. 

By-and-by he was able to go to school, where he 
passed through the usual routine of a good general 
education. No doubt his father's influence encour- 
aged him to the study of languages, of literature, and 
of philosophy. The quality of his mind, however, did 


not fit him for following in his father's footsteps. 
He had difficulty in acquiring languages, finding it 
hard to remember words, idiomatic expressions, and 
irregular grammatical forms. To have to commit 
prose to memory was torture, but he found it easy 
to store up passages of poetry, when he was helped 
by rhythm and rhyme. His father observed this 
peculiarity, and being himself an enthusiastic student 
of poetical literature, he introduced his boy to this 
golden storehouse, and not only read widely with 
him, but encouraged him to commit to memory poems 
and ballads from German literature. They read 
Homer together, and it is a remarkable indication of 
the breadth of his early education, that he was able to 
read the fables of L^kman in the original Arabic when 
he was twelve years of age. His father also exercised 
him in the composition of essays and even of verses, 
and Helmholtz remarks that although the verses 
showed that he was a poor poet, the practice was 
invaluable in the way of training him to the proper use 
of forms of expression. No doubt the home, if not 
scientific, was intellectual. He mentions that he fre- 
quently listened to philosophical discussions between 
his father and his friends, and thus he early became 
acquainted with some of the problems of metaphysics, 
as enunciated by Kant and Fichte. 

The mind of Helmholtz opened up, becoming more 
receptive and retentive when the world of nature was 
placed before him, and when he was introduced to 


phenomena. Already his wooden bricks had taught 
him much as to geometrical relationships. The mind 
became familiar with ideas as to spacial relations, and 
as to the adjustment of various forms, while he placed 
his bricks now in this position, now in that, so that 
when he began the systematic study of geometry at 
the Normal School of Potsdam in his eighth year, 
he astonished his teachers by his knowledge of many 
fundamental truths. He was already beginning to try 
his wings. 

As he became stronger in body, he was able to 
ramble with his father in the beautiful country around 
Potsdam, with its palaces and gardens, and he began to 
look at nature with his own eyes. Not only was the 
love of the beautiful in nature encouraged, but also the 
sense that all her operations were ruled by law. He 
was now attracted to physical phenomena more than to 
the abstract ideas of algebra and geometry, and he 
early realised that a knowledge of natural events and 
of the laws that regulate them was, as he says, the 
1 enchanted key ' that places the powers of nature in 
the hands of its possessor. Antiquated text-books of 
physical science found on the bookshelves of his father 
were eagerly read. His enthusiasm also found vent in 
attempts at experiment, to the detriment, he said, of 
his mother's furniture and linen. He constructed 
optical apparatus with a few spectacle glasses and a 
small botanical lens belonging to his father. While 
the class in the Gymnasium were reading Cicero 


or Virgil, most of which was tiresome to young 
Helmholtz, he was endeavouring, below the table, to 
work out problems and draw diagrams relating to the 
passage of rays of light through a telescope. Even 
then he worked out for himself some optical principles, 
not expounded in ordinary text-books, which were of 
use to him in later years, in the construction of the 
ophthalmoscope. This was his apprenticeship in the 
art of experimenting, in which he afterwards became 
so proficient a master. He learned how to think out 
the conditions of an experiment, turning the question 
round and round, so that he might view it on all sides, 
pondering over the possible ways of achieving the solu- 
tion of the mechanical or optical problem before him, 
until he got a clear idea of what had to be done. He 
also developed a passionate zeal to find out the realities 
of things, a zeal that continued throughout life, and 
appeared to grow in intensity as the years flew onwards. 
He was never satisfied with the apparent solution of a 
problem, if there were still doubtful points in it, and 
these he invariably attempted to clear up by bringing 
them fairly before his own mind. 

It has been said by one who knew him well at 
this early period of his life, that he was faithful to 
his duties in great as well as in small matters. He 
was zealous in his studies ; and in the autumn of 
1838, after the abiturienten examination, he left the 
Potsdam Gymnasium for the University with the 
following certificate from his Rector : 


* His exceptionally calm and reserved disposition is 
combined with great intellectual enthusiasm. In it 
we recognise an excellent combination of clear and 
prudent understanding and deep good nature. His 
manners bear witness to a carefully preserved, ex- 
ceptionally pure, and genuine childlike innocence. 
These peculiarities, along with the richness and 
power of his mental development, give an agreeable 
and captivating impression, and justify the hope that 
such a ground-soil of intellectual life will only bring 
forth the best of fruits.' This testamur and prophecy 
were amply justified in after life. 

It is remarkable that his mathematical talents were 
developed without the aid of an eminent teacher. 
He had no training in mathematics such as has 
been given to the great majority of physicists who 
have attained eminence. His talent was not fostered 
by the mathematical atmosphere of a great university 
like that of Cambridge, nor did he start life among 
his comrades with the blue ribbon of a high wrangler- 
ship. His mathematical development was silently 
carried on, so that some of his early friends, such as 
Briicke and Du Bois Reymond, both afterwards 
physiologists of the first rank, who were his fellow- 
students at the Gymnasium, were not aware, even 
when they were all engaged in the problems of 
analytical geometry, how transcendent were his 
latent mathematical powers. 

Such was his early training. Throughout life 


Helmholtz manifested the same mental character- 
istics as were shown in his early years. The same 
love of nature, the same desire to penetrate her 
secrets, the same determination to compel nature to 
explain herself. As is the case with most men of 
genius, he awakened early to his vocation. This 
awakening of a young spirit may come in many 
ways, and the time of its occurrence is always of 
the deepest interest. The youthful artist then 
recognises the beautiful, he clothes it with an ideal 
which is the product of his own mind, and to give 
to the ideal expression in form and colour is for ever 
the aim of his life. In like manner the young 
naturalist opens his eyes to the order of the universe, 
he is impressed by the majesty of law, he feels the 
first thrill of a desire to understand the method of 
nature's working, and for him, in all his future life, 
the driving power of all his faculties and the satis- 
faction of all his ideals, is the pursuit of truth. 



IT was the desire of Helmholtz to devote his life to 
the study of physics, but his father, who had, 
out of his limited means, to maintain a family of 
four children, showed him that it would be almost im- 
possible to earn a livelihood by cultivating or teaching 
pure science, and he wisely counselled his son to 
study medicine in the first instance. This advice was 
supported by the practical assistance of a relative, 
Surgeon-General Mursinna, who obtained for Helm- 
holtz admission in 1838 as a bursar into the Royal 
Medico-Chirurgical Friedrich-Wilhelm Institute in 
Berlin, an academy for the medical education of 
youths of promise, given freely on the condition 
that they afterwards become surgeons in the Prussian 
army. The students of this institution attended the 
usual courses of instruction in the medical department 
of the University, and were afterwards attached for 
a time to the Charit6 Hospital. Thus Helmholtz 
was, by force of circumstances, led to enter the 
medical profession, and in due time he obtained his 
diploma and became an army surgeon. 

In after life Helmholtz often referred to the great 


advantage he gained by being obliged to pass through 
the curriculum of medical study. In a famous lecture 
on Thought in Medicine, delivered in 1877, he remarked, 
' My own original inclination was towards physics ; 
external circumstances obliged me to commence 
the study of medicine. It had, however, been the 
custom of a former time to combine the study of 
medicine with that of the natural sciences, and what- 
ever in this was compulsory I must consider fortunate ; 
not merely that I entered medicine at a time in 
which any one who was even moderately at home 
in physical considerations found a virgin field for 
cultivation, but I consider the study of medicine to 
have been that training which preached more im- 
pressively and more convincingly than any other 
could have done, the everlasting principles of all 
scientific work ; principles which are so simple and 
yet are ever forgotten again ; so clear and yet 
always so hidden by a deceptive veil.' l 

The practical side of the medical art also appealed 
to his kindly nature. In the same lecture he remarks : 
1 Perhaps only he can appreciate the immense im- 
portance and the frightful practical scope of the 
problems of medical theory, who has watched the 
fading eye of approaching death, and witnessed the 
distracted grief of affection, and who has asked 
himself the solemn questions, Has all been done 
which could be done to ward off the dread event ? 

1 Popular Lectures, 1881, p. 202. 



Have all the resources and all the means which 
science has accumulated become exhausted ? ' l 

About this time there was a distinguished band of 
youthful students at the University of Berlin, who all 
ultimately became men of scientific eminence, and 
who made their mark on the learning of the follow- 
ing thirty or forty years. Here Helmholtz met Du 
Bois Reymond (a friend of his school days), who 
afterwards became Professor of Physiology in the Uni- 
versity of Berlin, and who systematised and developed 
the department of electro-physiology ; Briicke, who 
in due time was elected to the Chair of Physiology in 
Vienna ; Virchow, the greatest of living pathologists, 
who still holds the Chair of Pathology in Berlin, while, 
he is a power in science and also in the state ; and 
many others. These all clustered round the feet of 
the greatest physiologist of the time, Johannes Miiller, 
who taught anatomy and physiology in the university. 
It so happened also that Gustav Magnus rilled the 
Chair of Physics. These two distinguished men 
represented a new school of thought, then arising in 
Germany, that which rebelled against the older 
metaphysical school, and craved for the investigation 
of natural phenomena. They attracted many dis- 
ciples, and an alliance was established between the 
physicists and chemists on the one hand, and the 
physiologists on the other. Thus Gustav Karsten, 
Heintz, Knoblauch, Clausius, Kirchhoff, Quincke, 

1 Popular Lectures, op. cit. y p. 203. 


Werner Siemens, Tyndall and Wiedemann, who all 
became remarkable in chemistry or physics, joined 
Du Bois Reymond, Helmholtz, Briicke, and others, 
who represented the physiological school, in founding 
the Physical Society, a society in which they met on 
equal terms and freely discussed papers dealing with 
scientific questions. 1 It is impossible not to notice 
the great preponderance of physicists in the little 
band ; indeed it may be said they were all physicists, 
as Du Bois Reymond and Helmholtz, and even 
Briicke, approached physiological problems from the 
physical side. It was an epoch in the history of 
science, as not a little of the outcome of modern 
science, and, in particular, its methods, may be 
traced to that group of brilliant young men. 

There can be little doubt that Johannes Miiller 
was the greatest living force in the University of 
Berlin at that time. A man of indefatigable industry 
and perseverance, with an energy that overflowed 
into many sciences, a man of worthy aims and clear 
insight, who had the power of inspiring the youths 
who hung upon his words, a man who had in his 
great text-book collated and discussed the facts of 

1 Du Bois Reymond points out that Carl Ludwig was not a pupil of 
Johannes Miiller. He studied at Marburg and followed his own 
course, ultimately becoming Professor of Physiology in Leipzig. He 
became a physiologist of the highest eminence, and, both by his own 
labours and that of his numerous pupils, whom he attracted from all 
countries, advanced many departments of physiological science, in par- 
ticular our knowledge of the circulation of the blood. 


physiological science in a manner that in some re- 
spects resembled the great work of Haller, published 
a century before, Johannes Miiller was the greatest 
biological teacher of his time. In some ways he 
resembles John Hunter more than any other naturalist, 
but, owing to the circumstances in which he worked, 
he left behind him what Hunter did not leave a school 
of ardent disciples imbued with the spirit of the master. 

Miiller also gave a great impetus to the movement 
that had already begun in Germany in the direction 
of the investigation of biological problems by the 
methods of physical and chemical science. The 
principles of the Baconian philosophy took root and 
influenced science much later in Germany than in 
England ; and while in Germany there were, up to 
the time of Miiller, many workers who were in- 
fluenced by that school, the teaching of science, and 
even its investigation, more especially of physiological 
science, were still cramped by the speculative method 
of metaphysics. The fundamental problem of the 
nature of vital action was held generally to be 
beyond the domain of experimental science ; the 
doctrine of a vital force which modulated and held 
in subjection all other forces held sway ; and the 
great conception of the unity of origin of all the 
tissues of the body, established by the cell theory of 
Schleiden and Schwann, had not yet clearly dawned 
on the minds of physiologists. 

The influence of Miiller was felt throughout the 



world after the publication of his great text-book of 
physiology. Here were found not only all the facts 
of the science then known, but also the discussion 
of principles. In particular, the physiology of 
nerves, of nerve centres, and of the senses, was ex- 
pounded in a manner that hitherto had not been 
attempted. Miiller also laid the foundations of the 
school of modern experimental psychology by placing 
on a clear basis the mode of action of external 
stimuli on the terminal organs of sense. He showed 
that in whatever way a terminal organ is stimulated, 
the result is the same in consciousness, according to 
the nature of the particular terminal organ. Thus 
if we stimulate the retina of the eye by light, or 
electricity, or heat, or mechanical pressure, as by a 
blow, the result will always be the same namely, 
the sensation of a flash of light, possibly of colour. 
Further, the same result follows any kind of irritation 
of the optic nerve, which conveys the impulses from 
the retina to the brain ; and from this he deduced the 
great law of the specific sensibility of nerves, by 
which he meant that each nerve of special sense has, 
as it were, its own sensibility, so that, in whatever 
way it may be stimulated, the result will always be 
the same. This doctrine was especially fruitful in 
the hands of Helmholtz, Fechner, Briicke, Hering, 
and many others. It was a great step to recognise 
that the * sensation due to a particular nerve may 
vary in intensity, but not in quality, and therefore 


the analysis of the infinitely various states of sensation 
of which we are conscious must consist in ascertain- 
ing the number and nature of those simple sensations 
which, by entering into consciousness each in its 
own degree, constitute the actual state of feeling at 
any instant.' J There can be no doubt that in this 
and many other departments of physiological science, 
Miiller awakened new ideas and stimulated teachers 
of youth. Bowman, Sharpey, and Carpenter, in 
England ; Allen Thomson and John Goodsir, in 
Scotland ; Claude Bernard and Vulpian, in France ; 
Donders, in Holland, all felt his influence. Thus 
he prepared the way, not only for the labours of 
Helmholtz, and the other young men who were his 
immediate students, but for the remarkable development 
of physiological science that has taken place since 1840. 
Helmholtz long afterwards wrote words that apply 
with striking force both to his great master and to him- 
self. < When one comes into contact with a man of the 
first rank, his spiritual scale is changed for life. Such 
a contact is the most interesting event that life can offer.' 
In 1842, Helmholtz, at the age of twenty-one, pre- 
sented his inaugural thesis, entitled De Fabrica 
systematis nervosi Evertebratorum^ in which he made 
an important contribution to minute anatomy. In 
1833 Ehrenberg discovered in ganglia, which are 
usually small, more or less rounded swellings on 
nerves, often situated at the apparent junction of 

1 Clerk Maxwell on Helmholtz, Nature, vol. v., p. 389. 


several trunks, peculiar cells or corpuscles, now 
called nerve cells or nerve corpuscles. These cells 
are found also in all nerve centres, such as the spinal 
cord and brain, and they lie in a fine variety of tissue, 
while numerous nerve fibres pass through the ganglia, 
apparently in close proximity to the cells. No con- 
nection between the nerve cells and the nerve fibres 
had been discovered, although Miiller taught that 
in all probability such a connection existed. It was 
reserved to Helmholtz to make the discovery. With 
a very simple and primitive form of a compound 
microscope, almost as different from the splendid 
instruments of the present day as a cheap spyglass is 
from an astronomical telescope, he discovered in the 
ganglia of leeches and crabs that the nerve fibre 
originates from one of these corpuscles. This was 
an observation of fundamental importance as showing 
the connection between nerve fibre and nerve cell, 
and it has been extended throughout all nerve centres. 
The so-called axis cylinder of a nerve fibre, the 
central part of a nerve fibre, always originates from 
a process or pole or prolongation of a nerve cell. 

Du Bois Reymond mentions that, during his last 
year of medical study, Helmholtz had an attack of 
typhus fever, for which he was treated gratuitously 
in the hospital, while his small weekly allowance for 
board was continued. At the end of his illness 
Helmholtz found himself in possession of a little 
fund. This was expended in the purchase of the 


microscope which aided him in the research for his 
thesis. The incident throws light on the economy 
and simplicity of his life at this period. 

We have now traced Helmholtz to the beginning 
of his career as a contributor to science. From 1842, 
when his first paper was published, and when he was 
twenty-one years of age, on to 1 894, the year of his 
death, when he had reached the age of seventy-three, 
papers flowed from his pen in almost uninterrupted 
succession. With the exception of one year, 1849, 
he always published at least one important paper, and 
usually three or four, and occasionally more, each 
year, so that, when his life's work was over, no fewer 
than 217 distinct papers and books represented his 
labours. Such a life of incessant labour could not be 
expected to be full of incident. It is, therefore, 
difficult to portray his life step by step. There is 
not much to lay hold of in following his career ; 
we must be content with trying humbly to tread 
in his footsteps in the pathways of science, and to 
endeavour to grasp the scope and meaning of the 
many discoveries he made. The great variety of 
his work in so many sciences suggests the method 
of classifying his discoveries and then attempting 
to show the nature of his investigations in physi- 
ology, in physiological optics, in acoustics, in 
mathematics, in mechanics, in electrical science. 
This method, while it would give coherence to 
this work, would make a biographical sketch 


almost impossible, and it is open to the objection, that 
it would render each chapter a somewhat unsatis- 
factory resume of the science, without making us 
acquainted with the man. We prefer, therefore, in 
the following chapters to trace his career, as far as 
possible, by his works, as these were given to the 
world from his various spheres of activity. He spent 
his life in Berlin from 1842 to 1847, when he became, 
at the age of twenty-nine, Professor of Physiology in 
Konigsberg ; he was in Konigsberg from 1849 to 
1856, when, in his thirty-fifth year, he was removed 
to the Chair of Physiology in Bonn ; this he held 
till 1859, when, in his thirty-eighth year, he became 
Professor of Physiology in Heidelberg ; here he re- 
mained till 1871, when he was called to occupy the 
Chair of Physics in Berlin in his fiftieth year ; and 
this position he held until his death in 1894. It will 
give, we think, the best idea of the man to endeavour 
to cluster his discoveries round the centres where they 
were made. Thus we will see how his mind swung 
from one subject to another, and how his powers 
matured until he became a giant among his fellows. 
The method will also enable us to appreciate the 
value of his contributions to science with reference 
to the time and circumstances in which they were 
made. We will also see that while he was a master 
in medicine he was something more, and that at 
least seven sciences will hereafter claim Helmholtz 
as one of their most distinguished investigators. 



E adequate recognition of the work of a great 
man, in any sphere of intellectual activity, 
depends much on a correct appreciation of the streams 
of tendency apparent in the time before he appeared. 
We must endeavour to discover the lines along which 
thought was progressing, and to see, not from our 
standpoint, but from theirs, the questions which were 
then agitating the minds of men. This will enable 
us to estimate, on the one hand, the influence of the 
time upon the man, and the share that other men's 
thoughts had in moulding his character and directing 
his mental energies ; and, on the other hand, the extent 
to which he reacted on the conditions surrounding 
him, and the contributions he made to human know- 
ledge. Men of science, in particular, must be dealt 
with in this way. The state of education, especially in 
the universities, the facilities for scientific work, the 
current of scientific opinion, must all be studied before 
we can fairly judge as to what the man was, and as to 
what work he accomplished. One result from such 


an investigation is, that we see that the great thinker 
came at an opportune time. There are times in the 
history of science when there is a kind of quietism. 
Many busy workers are engaged in the accumulation 
of facts, but there are no startling discoveries nor broad 
generalisations that seem to put things in a new light. 
Such periods are unfavourable to the production of 
great men. Yet, even during such times, there may 
be undercurrents of thought making for great ques- 
tions. Here and there a solitary thinker may be 
brooding over great problems, and, although his 
thoughts may be dark, he is almost unconsciously pre- 
paring the way for the full revelation of the truth to 
the man of genius. Thus it is that to only a very 
few is vouchsafed the honour of making an entirely 
new discovery. This is an occurrence of the rarest 
kind. The rule is that limited observations of the 
truth are made here and there by men who are soon 
forgotten (except by the historian of science), vague 
and nebulous speculations, as it were, float in the air, 
and at last an epoch arrives, and with it the man. 
The epoch ushers in new ideas, new modes of looking 
at things, new generalisations of far-reaching char- 
acter affect the views of scientific thinkers, and with 
this new period we usually associate the name of one 
man, such as Copernicus, Galileo, Newton, Linnaeus, 
Darwin. Great, individually, as such men were, in 
estimating their work we must remember that they 
were not only highly endowed, but that they were 


also the children of good fortune. They came on the 
world's stage at the right time, they caught up all the 
impressions of the science of their day, they added to 
this the product of their own labours, and thus they 
gave a new impetus to scientific progress. 

The career of Helmholtz illustrates what has been 
written. To understand in some measure how he 
contributed so much to the science of his day, we 
must not only recognise his transcendent genius, but 
also that the times were favourable to its full develop- 

During the eighteenth and the beginning of the 
nineteenth century, science made little progress in 
Germany. l In chemistry the phlogiston theory led 
men in the wrong direction for nearly a century. The 
problems of physical science were still approached by 
the a priori method, and the speculations of Schelling 
and Hegel were not favourable to any method that 
had for its foundation the investigation of facts. Here 
and there important scientific results were obtained, 
such as Chladni's study of elastic vibrations of plates, 
Ritter's electrical experiments, and Seebeck's discovery 
of thermo-electricity, but there was no co-operation 
among the physicists, and there was no common goal 
towards which their energies were directed. 

Physiology had not yet asserted her existence as a 
science founded on observation and experiment. She 

1 G. Wiedemann, Introduction to Helmholtz's Wisienschaftliche 
Abhandlungen . Leipzig, 1895. 



was still the handmaid of anatomy, and she was domin- 
ated by the metaphysical idea of a vital force. This 
idea hindered investigators from examining many 
physiological phenomena which are under the same 
forces as those at work in the inorganic world, and the 
notion that vital actions were dependent on molecular 
and chemical changes in living tissues, had not yet 
been entertained. 

In France, however, science was not in this dormant 
state. The intellectual unrest, which culminated in 
the Revolution, led to almost universal scepticism, a 
state of mind which found expression in the writings 
of the Encyclopaedists. For a time men lost faith in 
the methods and conclusions of philosophical and 
ethical systems, and thought was determined towards 
physical and chemical science. Then arose Coulomb, 
Lavoisier, Laplace, Cuvier, and many others, and 
France became the leader in scientific investigation, 
more especially in physics and chemistry. This state 
of things was not without its influence on Germany. 
Many young scientific men from Germany, such as 
Alexander von Humboldt, Mitscherlich, and Liebig 
received their training in Paris, and imbibed the 
scientific spirit of the French savants. Such men 
returned to their own country, and soon occupied 
positions of influence in the universities. In these 
days, as now, Paris was to a large extent France, and 
this produced a concentration of scientific effort which 
did not take place till a later period in Germany, owing 


to the universities of the latter being scattered in the 
various states. By degrees, however, concentration 
also occurred in Germany. According to Wiedemann, 
an important school of mathematical physics arose in 
Konigsberg, and at last in Berlin, as in Paris, and 
largely owing to the influence and fame of Mitscher- 
lich, a scientific centre was formed. 

The earlier workers in the period of scientific 
awakening were such men as Mitscherlich and Liebig 
among chemists, and Ohm, Franz Neumann, and 
Wilhelm Weber among physicists. These were soon 
joined by the contingent from Berlin, which included 
Poggendorff, Riess, Dove, and Magnus. The latter, 
Magnus, became especially a notable teacher and 
laboratory worker, influencing both by teaching and 
example a number of young and able men. These 
physicists were in rebellion against the metaphysical 
schools which had so long dominated the thought of 
Germany, and they swung almost to the opposite 
extreme, extolling nothing but experience and experi- 
ment. For a time the collection of facts seemed to 
be the paramount object in physical research ; theory 
was in the background. So far did Magnus carry this 
view, that, as we are assured by Wiedemann, he was 
constantly warning his pupils not to plunge too deeply 
into mathematics, and he regarded experimental and 
mathematical physics as two separate departments. 
In this way, do doubt, the Berlin school built a firm 
foundation of fact for theoretical views, as distinguished 



from notions which were the outcome of metaphysics ; 
and the work on thermodynamics of Clausius, one of 
Magnus's distinguished pupils, is an apt illustration of 
this statement. As also pointed out by Wiedemann, 
the writings of Helmholtz and Robert Mayer are 
good examples, the first of theory developed from 
experiment, and the second of a more metaphysical 
mode of investigation. 

Empirical physical research has a tendency to become 
one-sided, and after it has been indulged in for a time, 
it is almost invariably followed by a more general 
treatment of the subject. This occurred among the 
disciples of Magnus. Earnest in their earlier years in 
the discovery of facts, in their latter they each and all 
were engaged in the contemplation of theoretical views 
then far beyond the range of experimental science. 

The rise of the physico-chemical school of Berlin 
had an important influence on the development of 
physiology in Germany. Ernst Heinrich Weber was 
no doubt the first to ask for an explanation of the 
phenomena of life by examination of these phenomena 
by physical methods, and the application of physical 
laws. After him came Johannes Miiller, who was at 
first somewhat wedded to the older quasi-metaphysical 
position, but in his later years he also took up the views 
and methods of Weber. For a considerable time, how- 
ever, the notion of a vital force still held sway. Pheno- 
mena in living things were supposed to be different 
not only in degree, but in kind, from those in inorganic 
2 3 


matter. If this notion were to be got rid of, it could 
only be by prolonged investigation in a physico- 
chemical direction. Such were the views of three 
young physicists and physiologists, Briicke, Du Bois 
Reymond and Helmholtz. As already narrated, 
these three joined the physicists and chemists in 
founding the Physical Society of Berlin. Here they 
found sympathy and encouragement. Here papers 
were read and frankly criticised. Here was de- 
veloped, for the first time, an attempt to investigate 
physiological phenomena by the methods of chemistry 
and physics. Physiology, indeed, was regarded as in a 
sense a branch of chemico-physics, and the phenomena 
of nature chemical, physical, physiological were held 
to be controlled by one general principle, or rather to 
depend ultimately on the properties of matter. Some 
of these enthusiasts took even a wider sweep, and 
brought into their net the phenomena of psycho- 
physics, and the physical and physiological foundations 
of the arts sculpture, painting and music. 

Helmholtz was without doubt the most distinguished 
of this group of young men. He was, to use Wiede- 
mann's expression, and Wiedemann was a contem- 
porary, head and shoulders above the rest. In each 
department of scientific labour represented by the 
members of this brilliant galaxy, he acquired, in after 
life, marked distinction ; to each department he made 
vast additions, while he elevated the whole body of 
scientific knowledge. 





DURING the greater part of the period from his 
graduation in medicine in 1842 till his appoint- 
ment to the Chair of Physiology in Konigsberg in 
1849, Helmholtz resided in Berlin. He completed 
his term of service as assistant physician in the La 
Charite Hospital, and, in 1843, he returned to Pots- 
dam, where he discharged the duties of assistant surgeon 
to the regiment of Red Hussars. Private practice he 
never had ; all his time, when off duty, being devoted 
to science. Coming under the notice of Alexander von 
Humboldt, that great man recognised his capacity, 
and through his influence he was relieved from mili- 
tary duties, and became assistant to the Anatomical 
Museum, Lecturer on Anatomy to the Academy of 
Arts, and Extraordinary Professor of Physiology to 
the Albert University. In the two latter appoint- 
ments it is interesting to know that he succeeded his 
friend Ernst Briicke, who subsequently filled with 
great distinction the Chair of Physiology in Vienna. 
There is little doubt the appointment to the Academy 


gave his mind the aesthetic bias so apparent in after 
years. His researches, however, were not anatomical, 
but physiological and physical. 

In 1843 ne mac le an important contribution to the 
theory of fermentation. This process has long been, 
and indeed still is, the cause of much controversy 
between chemical physicists and biologists, and from 
the controversy has flowed results of the highest 
importance to humanity. When sugar is changed 
into alcohol and carbonic acid in the ordinary alcoholic 
fermentation, the process is in some way related to 
the vegetable cells of the yeast plant, Saccharomycetes 
cerevisiee^ first seen by Leeuwenhoek in 1680. For 
many years these minute organisms received little or 
no attention, but in 1838 Schwann, one of the 
founders of the cell theory, and Cagniard de la Tour 
demonstrated the vegetable nature of these yeast cells, 
and showed that they grew and multiplied in saccharine 
solutions. For the first time it was asserted that 
fementation in some way depended on the action of 
living things. Previous to 1838 Berzelius suggested 
that the action of the yeast is what is called catalytic, 
that is causing a separation or decomposition of the 
atoms forming the sugar in a way similar to the 
action of platinum black on peroxide of hydrogen, 
when the latter gives up an atom of hydrogen. 
Liebig strongly contended that there is no necessary 
connection between the fermentive process and the 
development of living organisms, and he held that the 


organisms may simply produce a substance, the mole- 
cular vibrations of which may cause a re-arrangement 
of the atoms of the substance undergoing fermenta- 
tion. According to this view fermentation is essenti- 
ally a chemical process. A substance of unstable 
chemical composition is formed by the yeast cells, 
and by vibrations, due to chemical changes in this 
substance, movements are communicated to the atoms 
of sugar, so that these are re-arranged to form alcohol, 
carbonic acid, and small quantities of a few other 
bodies. The growth of the yeast cell is only in- 
directly connected with fermentation. 

For a considerable time this theory held its ground, 
owing largely to the prestige of its illustrious author; 
but facts came to light that again concentrated the 
attention on the biological aspect of fermentation. 
Thus Gay-Lussac showed that clean grapes or boiled 
grape juice passed into the Torricellian vacuum of 
a barometer tube kept free from fermentation for any 
length of time, but that if a single bubble of air 
were admitted fermentation soon appeared. About 
1838 Schwann repeated Gay-Lussac's experiment, and 
showed that if the air were admitted to the vacuum 
through a red hot tube then fermentation did not 
occur. Clearly it was something in the air that 
caused fermentation, and that something was destroyed 
by heat. Further, it was shown that active fermentation 
was always accompanied by increased growth of the 
yeast, and that conditions of temperature affected the 


process. Thus a temperature of from 20 C. to 24 
C. was most favourable to it, while the process was 
arrested at 60 C. Boiling destroyed fermentation. 
It was also arrested by freezing, but on careful thaw- 
ing the process was resumed. Schwann also estab- 
lished the identity of the processes of fermentation 
and putrefaction by showing that they both were 
connected with the development of living organisms, 
and he laid the foundation for the splendid researches 
of Pasteur, which have created the modern science of 

The contribution made to this discussion by Helm- 
holtz in 1843 is of no mean importance. He showed, 
first, that the oxygen produced by electrolysis in a 
sealed-up tube containing boiled fermentable fluid, 
did not cause fermentation. He also performed the 
following ingenious experiment : he placed a bladder 
full of boiled grape juice in a vat of fermenting juice, 
and found that the fluid in the bladder did not ferment. 
Thus the cause of the fermentation could not pass 
through the wall of the bladder. If the fermentation 
were excited, as held by Liebig, by a substance formed 
by the yeast cells, and presumably soluble, one would 
have expected it to pass through the wall of the 
bladder ; but if the process were caused by the small 
yeast cells, then one can see why fermentation was 
not excited, as the yeast cells could not pass through 
the membrane. Soon afterwards Mitscherlich showed 
that the yeast cells could not pass through a septum 


of filter paper ; Hoffmann proved that a layer of cotton 
wool had the same effect ; and Schroeder and Dusch 
made the important demonstration, that air filtered 
through cotton wool is incapable of exciting putre- 
faction in a putrescible fluid that has been boiled. 
The cotton wool has sifted from the air the bodies 
that cause putrefaction, just as the wall of the bladder, 
the septum of filter paper, or the layer of cotton wool, 
prevents the passage of the yeast cells from a fermenting 
to a fermentable fluid. The conclusion, then, is irresist- 
ible that the living organisms in the air and in the yeast 
are the cause of putrefaction and fermentation. It will 
thus be seen that the comparatively simple observa- 
tions of Helmholtz, were of fundamental importance. 

Surrounded as he was by young physicists, it is 
not surprising that Helmholtz approached physiology 
on its physical side. Physiology is essentially a com- 
posite science, inasmuch as it is closely related to 
anatomy, physics and chemistry. In the solution of 
physiological questions, the physiologist must collect 
facts from these three departments of knowledge. 
Thus, for example, in investigating the phenomena of 
the circulation of the blood, the physiologist, in the 
first place, must be acquainted with the structure of 
the heart and blood vessels, with the position and 
appearances of the valves in the heart and in many of 
the veins, and with the nature of the minute texture 
or tissue of the heart, as revealed by the microscope. 
Then he considers the circulation as a problem of 


hydrodynamics, investigating and measuring the force 
and frequency of the heart's contractions, and deter- 
mining the causes of the high pressure maintained in 
the arterial system, the nature of the pulse, and the 
uniform flow of the blood in the capillaries. These 
investigations are all of a physical character. Finally, 
if the physiologist pursues his analysis still farther, 
he may examine the chemical characteristics of the 
tissues forming the heart and vessels, the nature of 
chemical compounds, both organic and inorganic, 
existing in these tissues, and the influence of chemical 
substances upon the living heart. Almost every 
physiological problem may be attacked in a similar 
way, and it can only be fully solved when all the 
information derived from anatomy, chemistry and 
physics is brought to bear upon it. It .will also be 
evident that some physiologists are attracted to one 
aspect of the subject, while others are drawn to 
another. One man endeavours to explore the mystery 
of living action by the microscopical examination of 
tissues, living and dead ; another works at the chemical 
constitution of organs and tissues, and tries to get a 
glimpse into the nature of the chemical processes 
associated with life ; while a third investigates the 
phenomena as special problems in physics. Helmholtz 
was an outstanding representative of the latter class, 
and he was so largely by reason of his special aptitude 
for physical and mathematical research, and of his 
surroundings. He might properly be described, even 


at this early stage of his career, as a highly-trained 
physicist interested in physiological pursuits. 

It is interesting to observe, that while physiology is 
largely indebted to physics, the latter science owes not 
a little to physiology, inasmuch as the consideration of 
physiological phenomena has, on several notable occa- 
sions, led the physicist into a new and fruitful line of re- 
search. The beginning of modern electrical science 
will for ever be traced back to the well-known observa- 
tions of Galvani on the twitching of frogs' legs near 
an electrical machine, to his speculations on the exist- 
ence of an animal electricity, and to the celebrated 
controversy that arose between Galvani and Volta, a 
controversy in which many of the most learned 
physicists and physiologists of the day took part. In 
like manner, the discussion of questions as to the 
nature of animal heat contributed not a little to the 
doctrine of the conservation of energy. Helmholtz 
took a foremost part in this movement, and there 
can be no doubt he was led into it, in the first 
instance, by physiological considerations. 

The physical properties of dead matter are, as a 
rule, more easily observed and registered than the 
physiological properties of living matter, and they lend 
themselves more readily to mathematical investigation. 
Hence physical science is much farther advanced than 
physiological science. The physicist is surer of his 
ground. The physiologist has to deal with the 
mysterious condition we call vitality. It is therefore 
3 1 


not astonishing that physicists, as a rule, are shy of 
dealing with physiological problems, and that they 
regard many of them as practically insoluble. In the 
judgment of the physicist, life, vitality, the mysteri- 
ous something apparently unknowable, so interferes 
with and obscures the play of the ordinary physical 
forces, as to lead him to doubt whether the physical 
phenomena of living matter can ever be thoroughly 
understood. Now it is remarkable that, although 
Helmholtz was already at the age of twenty-five a 
great physicist, he boldly entered on physiological 
research with the assured conviction that the play of 
the physical forces in living matter was under the 
same laws as in dead matter, and that the only way to 
investigate, with success, the phenomena of living 
matter, was to examine them by physical methods, and 
to submit them, as far as possible, to physical analysis. 
It was in this spirit that he began to investigate the 
phenomena of animal heat, and this investigation led 
him to lay the foundations of the great doctrine of the 
conservation of energy. The subject occupied much 
of his attention from 1844 to 1848, and he returned 
to it in 1850, 1852, 1855 and 1859. The old view 
that heat was a variety of imponderable matter had 
been attacked long before by Voltaire, who, in a series 
of elaborate experiments, endeavoured to prove that it 
was only a kind of internal movement ; and in 1798 
Count Rumford, one of the founders of the Royal 
Institution, after executing a series of experiments on 


the production of heat by friction, established, in a 
comparatively rough way, the dynamical theory of 
heat, in which heat is regarded as an accident or con- 
dition of matter, a phenomenon produced by ' a motion 
of its ultimate particles.' 

Helmholtz studied the exchanges of matter that 
occur in connection with muscular contractions, and 
he made the important observation, that such ex- 
changes are always accompanied by the disengagement 
of heat. This indicated that animal heat, as produced 
by a muscle, arises from the chemical phenomena 
occurring in the muscle. Before this research, Mat- 
teucci had apparently shown the production of heat 
during muscular contraction by passing thermo-electric 
needles into the muscles of a living warm-blooded 
animal, and connecting the needles with a thermal 
galvanometer ; but as in his experiments the blood was 
flowing through the muscle, the proof that the in- 
crease of temperature observed during the muscular 
contraction was due to changes in the muscle itself was 
not complete. Helmholtz got rid of the difficulty of 
having to deal with an organ through which streams of 
blood, possibly of different temperatures, were flowing, 
by making observations on the isolated muscles of 
c the old martyr of science,' the frog. He devised a 
triple thermo-electric junction of iron and German 
silver, so made that it could be passed through the 
muscles of the thigh of a frog. A similar set of 
junctions were kept at a temperature as uniform as 


possible, outside the muscles of the frog, and the two 
sets of junctions were connected with a thermal 
galvanometer, so sensitive, that deflections equivalent 
in thermal value to the y^-th of a degree Centigrade 
could be detected. When the muscles were caused to 
contract, by electrically stimulating the sciatic nerve, 
the junctions in the muscle became warmer than 
those outside the muscle, as indicated by a deflection 
of the needle of the galvanometer, and as the galvano- 
meter had been empirically graduated, the actual rise 
of temperature was at once estimated. It was thus 
shown that a single muscular contraction would give an 
increase of from '001 C. to '005 C., and that tetanus, 
or cramp, lasting for two to three minutes, would 
cause a rise of from '014 C. to 'Oi8 C. He failed, 
however, to detect heat in active nerves. These 
quantities of heat are no doubt small, but their detec- 
tion showed that the molecular processes occurring 
in the contracting muscle actually produce heat. 

Helmholtz also extended his observations to the 
general phenomena of animal heat. On Lavoisier's 
assumption that the amount of heat liberated could 
be determined by the quantities of oxygen consumed 
and of carbonic acid produced, it had hitherto been 
found that there was a discrepancy between the 
amount of heat actually given ofF by the body of an 
animal in a given time and the amount to be expected 
from calculation. The calculated amount of heat 
was usually more than that given off the living body. 


Helmholtz showed that less heat might be given off 
than could be estimated from the complete oxidation 
of the food supplied, indicating that the oxidation 
processes in the body were incomplete. He also 
computed the amount of heat given off by various 
channels as 2*6 per cent, in heating excrementitious 
matters, 2'6 per cent, in warming the air of expira- 
tion, 14*7 per cent, by evaporation of the lungs, and 
80* i per cent, by evaporation of sweat and radiation 
and conduction by the skin. These results have been 
corroborated and extended by many subsequent ob- 
servers, and it has been conclusively established that 
the heat of the combustion of the food, as determined 
by a calorimeter, is equal to the heat given off by an 
animal ; in short, that an animal is a living calorimeter 
in which the food stuffs are oxidised or burnt. 

A new investigation almost invariably demands the 
use of new appliances. New ideas, new conceptions 
of method, spring up in the mind of the experimenter, 
and a call is at once made on his powers of invention. 
This is felt even in a well-furnished laboratory, and of 
course much more when the investigator enters on 
what is a virgin field of research. Helmholtz, when 
he began the investigation of muscular contraction, 
had to invent many of his tools. About this period 
his friend, Du Bois Reymond, was laying the founda- 
tions of his life-long work on electro-physiology, and 
he also invented many appliances. There is little 
doubt Helmholtz and he assisted each other in de- 


vising apparatus by which the phenomena of muscular 
contraction could be accurately studied. Employing 
the method of causing a contracting muscle to write 
its curve on the blackened surface of a revolving 
cylinder, or on a moving glass plate, a method of 
observing the time relations of motor phenomena 
first suggested by Thomas Young, Helmholtz de- 
vised the well-known myograph, or muscle writer. 
Schwann had already worked with a rude instrument, 
in which the contracting muscle was caused to pull on 
a lever near its fulcrum, and no doubt he was the first 
to obtain a muscle curve, but Helmholtz improved the 
instrument by making the lever light, and at the same 
time rigid, and by other mechanical contrivances. 
Further, he endeavoured to keep the living muscle in 
conditions as favourable as possible by covering the 
part of the apparatus containing the muscle with 
a glass case, under which pieces of blotting paper, 
moistened with water, were placed. This 4 moist 
chamber,' as it is technically called, became a space 
saturated with aqueous vapour, and thus the muscle 
and nerve were kept in fairly natural conditions, and 
the effects of cooling and drying were obviated. 

Helmholtz also, in connection with this research, 
made arrangements by which the nerve or muscle 
could be stimulated by electric shocks of short dura- 
tion and of a known intensity. He applied to the 
well-known induction coil of Du Bois Reymond, 
designed for physiological purposes, a modification of 


Neef's interrupter, by which the circuit in the 
primary coil was opened and closed, and as the inter- 
rupter works automatically, a rapid series of shocks 
may be transmitted to the nerve or muscle. It was 
soon found that, with this arrangement, the opening 
shock acts more powerfully on the muscle than the 
closing shock, in other words, the opening shock has 
the greater intensity. This arises from the develop- 
ment, at the moment of closing the primary current, 
of an extra current in the primary coil, which, being 
in the reverse direction to that of the main primary 
current, so retards the development of the latter as to 
prolong the time during which the secondary current 
flows, and thus make it pass through a lower maxi- 
mum intensity than is reached by the secondary 
current at opening when the change of the primary is 
more abrupt, and the secondary current lasts for a 
correspondingly shorter time. The total quantity of 
current coming from the secondary coil is the same 
whether the primary circuit is being opened or 
closed ; but the secondary current, excited at opening, 
attains momentarily a greater intensity. Hence the 
opening shock is the more stimulating. As in stimu- 
lating a nerve or muscle by an induction coil it is 
important to stimulate with rapid opening and closing 
shocks of the same intensity^ Helmholtz so modified 
the Neef's interrupter as to equalise the currents. 
By his arrangement the current in the primary circuit 
is not wholly cut off. It is merely short-circuited. 


Thus the primary circuit is always closed ; but the 
decrease of current at the instant of short-circuiting 
has the same kind of effect in producing a secondary 
current as when the primary circuit is completely 
opened. But because the primary circuit remains a 
closed circuit, the extra current of self-induction 
retards the rate at which the current decreases, just as 
the extra current retards the development of the 
current at closing. Thus, the conditions under 
which the secondary currents at closing and at 
opening are produced are fairly similar ; the intervals 
of time during which they last are approximately 
equal ; and the maximum intensities reached by them 
are almost exactly the same. In this way the opening 
shock becomes nearly equal to the shock from the 
secondary coil at the moment of closing. 1 This 
clever device is a good illustration of the ingenuity 
of Helmholtz and of his grasp of the technique of 
electrical experimentation. 

1 For details, see M'Kendrick's Text-Book of Physiology, vol. i., p. 374. 
Glasgow, 1888. 



THE researches on muscular motion and on heat 
led Helmholtz to the study of the great 
question of the relation to each other of the forces 
of nature, and especially, and in the first instance, 
to the relation of these forces to the phenomena of 
life. What is life ? was a problem often before his 
mind. Was the living state to be explained by the 
interplay of the same chemical and physical forces 
as were at work in the outer world ? Or, was Stahl's 
view to be accepted, that while the forces were the 
same in living as in dead matter, they were all 
subject to a living power or principle which held 
them together and caused them to work in a particular 
way till death came, when the physical and chemical 
forces, now liberated from control, assumed their 
supremacy and the matter forming the body again 
returned to the inorganic world ? Was the energy 
of life continually replenished from some external 
source ; or was it dependent on the energy of the 


forces of nature supplied to it from the outer world ? 
Was the living body, in short, only a minute portion 
of the mechanism of the cosmos ; or was there some- 
thing beyond, some spiritual fuel continually being 
added to its vital fires ? Helmholtz thought that if 
the life was fed from some such source of external 
energy, then the living body was an example of a 
perpetuum mobile, a perpetual motion, an idea he had 
often heard ridiculed in the philosophical discussions 
that were not infrequent in his father's home. 

If, again, the natural forces were found competent 
to explain the phenomena of life without the assump- 
tion of a vital force, how were these forces related to 
each other ? About this period Helmholtz filled the 
humble office of assistant in the library of the Friedrich 
Wilhelm Institute, and in what he modestly terms 
his < idle moments,' he had read the works of Euler, 
Daniel Bernoulli, d'Alembert, and other mathe- 
maticians of the eighteenth century, no mean in- 
dication of his mathematical powers, and he thus 
became equipped for the discussion of the great 
question. He was especially acquainted with the 
manifold applications made by Daniel Bernoulli, of 
Leibnitz's idea of vis viva. 

Such considerations led Helmholtz, in his twenty- 
sixth year, to write his famous essay, Ueber die Erhaltung 
der Kraft on the Conservation of Force one of the 
epoch-making scientific papers of the century. Clerk 
Maxwell has well said : * To appreciate the full 


scientific value of Helmholtz's little essay on the 
Conservation of Force, we should have to ask those 
to whom we owe the greatest discoveries in thermo- 
dynamics and other branches of modern physics, how 
many times they have read it over, and how often 
during their researches they felt the weighty state- 
ments of Helmholtz acting on their minds like an 
irresistible driving power ? ' I 

The essay was read to the Physical Society of 
Berlin on the 23rd of July 1847, an( ^ lt created much 
excitement in the distinguished band of youthful 
workers. The author showed himself, at one stroke, 
to be a mathematician of the first order, but he also 
enunciated as a fundamental principle of physics the 
conservation of force, just as Lavoisier, seventy years 
before, had made that of the persistence of matter the 
fundamental principle of chemistry. He showed that 
* if the forces acting between material bodies were equi- 
valent to attractions or repulsions between the particles 
of these bodies, the intensity of which depends only on 
the distance, then the configuration and motion of 
any material system would be subject to a certain 
equation, which, when expressed in words, is the 
principle of the conservation of energy.' 2 In less 
technical language, he established mathematically that 
'force' (Kraft], or, as it is now termed, energy, is 
indestructible, and he shows that this principle 'con- 
tradicts no known parts of science, while it is con- 

1 Nature, op, cit. - Clerk Maxwell, Nature, op, cit. 

4 1 


firmed in a striking manner in a great number of 
instances.' Hence it follows that the total quantity 
of energy or capacity for work in the universe is 
constant, and remains eternal and unchanged through- 
out all the vicissitudes of matter. Energy can change 
its form and locality without its quantity being 
changed. The universe possesses a store of energy 
which is not altered by any change of phenomena, 
and the quantity can neither be increased nor 
diminished. Fifteen years afterwards, in 1862, 
Helmholtz, in a lecture, thus states the principle : 
c If a certain quantity of mechanical work is lost, we 
obtain an equivalent quantity of heat or of chemical 
force, and, conversely, when heat is lost we gain an 
equivalent quantity of chemical or mechanical force ; 
and, again, when chemical force disappears, an 
equivalent of heat or work ; so that, in all these 
interchanges between various inorganic natural forces, 
working force may indeed disappear in one form, 
but then it reappears in exactly equivalent quantity 
in some other form ; it is thus neither increased nor 
diminished, but always remains in exactly the same 
quantity. . . . The same law holds good also for 
processes in organic nature, so far as the facts have 
been tested.' I [For the word ' force ' it would be 
better to use the term c energy.'] 

Such a conception of the material world met 
with much opposition. The older physicists of 

? Helmholtz's Popular Scientific Lectures, 1873, p. 360. 


Berlin Dove and Riess would not admit the 
principle ; Magnus modestly declined to express an 
opinion, as he thought there should be a distinction 
between mathematical and experimental physics ; the 
mathematicians shook their heads, and we have it 
on the authority of Du Bois Reymond that only 
Jacobi, who himself had done excellent work in 
mechanics, saw its truth. Helmholtz, referring in 
after years to this opposition, said he was met by 
some of the older men by such a remark as this, 
' This has already been well known to us ; 
what does this young medical man imagine when 
he thinks it necessary to explain so minutely all this 
to us ? ' Poggendorff actually refused to insert the 
memoir in his famous periodical Annalen^ on the 
ground of its theoretical character. Du Bois 
Reymond took the manuscript to the publisher, 
George Ernest Reimer, then engaged in bringing 
out Du Bois's famous papers on animal electricity, and 
he not only published the paper, but gave Helmholtz 
a honorarium, a pecuniary recognition seldom awarded 
to an abstruse scientific work. The value of the 
work was soon recognised by the military authorities ; 
Helmholtz became a marked man ; and with the 
characteristic aptitude of the Germans for putting 
the right man in the right place, he was relieved 
largely from military duties, and encouraged to go 
on with purely scientific work. KirchhofF, Clausius, 
Du Bois Reymond, and others of the young and 


brilliant school, were enthusiastic in their approbation. 
Du Bois Reymond remarks, with some humour, 
1 His supporters declared that he had set in motion 
the conservation of another force, much more in- 
teresting for us, the mind of Helmholtz himself.' l 

It is now a matter of common knowledge, that 
while the principle of the conservation of energy 
slowly unfolded itself to the minds of the great 
scientific thinkers of the earlier part of this century, 
the root of the idea must be traced back to the in- 
tellectual giants Newton, Descartes and Leibnitz. 
Professor Tait has shown that Newton undoubtedly 2 
was in possession of the principal facts of the con- 
servation and transformation of energy. In the 
expression of his third law of motion, c to every action 
there is always an equal and contrary reaction,' the words 
'action ' and ' reaction' are interpreted by Newton him- 
self in two senses. Between any two bodies connected 
together, such as a weight resting on a table, there is 
always an equal and opposite reaction. The weight 
presses on the table and the table presses on the 
weight. Two bodies may also be connected by some 
invisible link, such as exists between bodies that are 
affected by magnetic attraction, and yet the law 
holds good. But action and reaction may occur in 
another sense. 'If the activity of an agent be 

1 Du Bois Raymond's Gedachtnissrede. Berlin, 1 896. 

2 Tait's Lectures on Recent Advances in Physical Science, 1885. Lect. 
ii., p. 27. London, 1885. 



measured by the product of its force into its velocity, 
and if similarly the counter activity of the resistance 
be measured by the velocities of its several parts 
multiplied into their several forces, whether these 
arise from friction, cohesion, weight or acceleration, 
activity and counter activity in all combinations of 
machines will be equal and opposite.' In overcoming 
resistance, as when work is spent in altering the 
shape of a body, work is done against the elastic 
forces of the body worked against, and, according to 
Newton's statement, the amount of work spent, or 
the rate of spending work in distorting the body, is 
equal to the amount of work done or the rate of 
doing work against the elastic forces. The work is 
stored up in the distorted body as potential energy. 
Suppose, again, work is expended in a body where 
there is no resistance from friction, cohesion or 
weight, it will be spent in overcoming the inertia of 
a body and increasing its velocity, that is to say, the 
kinetic energy of the body increases. In such a case 
the ' rate at which work is spent is measured by the 
product of the momentum into the acceleration in the 
direction of the motion.' We know that when 
work is done against friction, an amount of heat is 
produced exactly proportional to the amount of work 
expended. In Newton's day, this had not been 
experimentally proved ; otherwise Newton would 
probably have definitely formulated the law of the 
conservation of energy. As Professor Tait says 


' What Newton really wanted then was to know 
what becomes of work that is spent in friction.' 

Descartes affirmed the doctrine of the constancy of 
the quantity of motion, that is of momentum, in the 
world. Leibnitz, in whose dynamical views of nature 
force was the ultimate reality, contended that Des- 
cartes's statement, that motion is measured by velocity, 
should be abandoned for the conception of a vis 
matrix^ a moving force measured by the square of the 
velocity. He enunciated in 1686 the principle of 
the conservation of vis viva^ and came near a full 
mathematical expression of the law of the conserva- 
tion of energy. Both Descartes and Leibnitz were 
correct in their contentions, and the principle of 
Descartes may be called the conservation of momen- 
tum, while that of Leibnitz is a partial statement 
of the conservation of energy. 1 

The discussion is closely connected with the views 
held by thinkers regarding the nature of heat. Thus 
Bacon wrote : ' Heat is a motion, expansive, re- 
strained, and acting in its strife upon the smaller 
particles of matter.' 2 

John Locke, by a priori reasoning, had also made a 
happy guess, that heat was not matter but motion, 
that it 'was a brisk agitation of the particles of 
matter,' but the statement was unsupported by 
experimental evidence. 

1 Sorley, Art. Leibnitz in Encyd. Britaim., vol. xiv., p. 422. 

2 Bacon, Spedding's Translation, vol. iv. 

4 6 


About 1798 Count Rumford performed his famous 
experiments on the boring of cannon, and he observed 
that the heat produced was much greater than that 
of boiling water. The older theorists held that heat 
was a substance, but Rumford's work went far to 
prove that it was not matter. The proof was 
conclusively given by Humphry Davy, who ob- 
tained sufficient heat to melt ice by rubbing 
two pieces of ice together. In 1812 Davy wrote: 
' The immediate cause of the phenomena of heat, 
then, is motion, and the laws of its communication 
are precisely the same as the laws of the communi- 
cation of motion.' Professor Tait remarks in this 
connection : ' If Davy had with this statement 
taken into account the second interpretation of 
Newton's third law, the dynamical theory of heat 
would have been his.' 

It is said that Montgolfier entertained the idea of 
the equivalence of heat and mechanical work, and his 
nephew Seguin performed experiments with a steam 
engine, in which he endeavoured to ascertain whether 
the same quantity of heat reached the condenser as 
had left the boiler. Had he succeeded in showing 
that less heat reaches the condenser than had left 
the boiler, he would have found that the heat 
apparently lost was in proportion to the mechanical 
work performed by the engine. 

The notion of the correlation of the physical forces 
was slowly shaping itself. Mrs Somerville's book on 


the Connection of the Physical Sciences was published 
in 1834, but little is said about the 'connections,' 
except that a knowledge of one science is often 
essential to the successful prosecution of another. 
In January 1842, Grove delivered a lecture in the 
London Institution on the Correlation of the Physical 
Forces, which was afterwards expanded into a well- 
known volume. This work shows that of the 
various forms of energy existing in nature, any one 
may be transformed into any other, the one form 
appearing as the other disappears. No doubt this 
book, written in a clear and lambent style, familiarised 
the public mind with the new conception, and it 
also influenced scientific opinion. Clerk Maxwell 
says of this epoch in the history of science : * The 
fathers of dynamical science found a number of 
words in common use expressive of action and the 
results of action, such as force, power, action, impulse, 
impetus, stress, strain, work, energy. They also had 
in their minds a number of ideas to be expressed, and 
they appropriated these words as they best could to 
express the ideas. The words force, vis, kraft, came 
most readily to hand.' 

In and about 1842 the speculations and researches 
of Robert Mayer of Heilbronn appeared. Only to a 
limited degree an experimenter, Mayer had yet 
wonderful clearness of vision and originality, and 
although his premises were sometimes inadmissible, 
and his reasoning faulty, he enunciated a true 


theory and developed its applications, more especially 
in the organic world. He gave a popular exposition 
of the theory of the transformation of energy into 
heat, and he even calculated the dynamical equivalent 
of heat, 1 giving it as 365 kilogramme-meters, instead 
of the true equivalent, ascertained experimentally by 
Joule to be 425 kilogramme-meters, for iC. (equivalent 
to 772 foot-pounds for i F.). His papers produced 
little effect, even in Germany, at the time of their 
publication, partly because they were founded so little 
on experimental enquiry, and partly because they 
were the work of an obscure physician in a country 
town. His writings had no influence on science 
until long after the truth had been proclaimed by 
Helmholtz. The science of energy would have 
progressed much as it has done had Mayer never 
lived ; but, on the other hand, had the doctrine of 
the conservation of energy come first from Mayer, 
there would still have been the need of a mathe- 
matical thinker like Helmholtz to establish it as a 
law of nature. It is only fair to mention Mayer's 
obscure position (no fault of his) as an explanation 
of the fact that, when Helmholtz wrote his essay, 
he was totally unacquainted with Mayer's work. 
When, in subsequent years, it was brought under 
his notice, no one was more generous than 
Helmholtz in his estimation of the merits of his 

1 Mayer, Lietig's Annalen, vol. xlii., p. 233 ; Phil. Mag,, 4th series, 
vol. xxiv., p. 371 5 Resume m PAH. Mag., xxv., p. 378. 


compatriot ; and the question of priority, which was 
for a time keenly discussed by the friends of 
both parties, was one that gave no concern to 
his great mind. It is said that he bestowed even 
more credit on Mayer than the latter claimed for 

The theory of the conservation of energy was 
established experimentally by Colding of Copenhagen 
and Joule of Manchester. The works of Sadi Carnot 
(1824) and Clapeyron ^1833) in France in relation 
to heat were also of first-rate importance. Carnot 
had shown that work was done where heat was 
transmitted from a body of a higher temperature to 
a body of lower temperature. The Danish philo- 
sopher was less of an experimenter than Joule, but 
he expresses his conclusions in the following unmis- 
takable language : 

' Force is imperishable and immortal ; and, therefore, 
where and wherever force seems to vanish in perform- 
ing certain mechanical, chemical or other work, the 
force then merely undergoes a transformation and re- 
appears in a new form, but of the orginal amount, as an 
active force. 1 In the year 1843 this idea, which com- 
pletely constitutes the new principle of the perpetuity 
of energy, was distinctly given to me, the idea itself 
having been clear to my own mind nearly four 
years before, when it arose at once in my mind by 

1 Colding's Treatise, 1843, Royal Society of Copenhagen. Theses con- 
cerning Force. Nogle, Saetninger om Krcefterne. 


studying d'Alembert's celebrated and successful 
enunciation of the principle of active and lost 
forces ; but, of course, the new principle was not as 
clear to me from the beginning as it was when I 
wrote my treatise in 1843. I closed m y discussion 
by showing that the discovery of a perpetuum mobile 
would be possible if my principle was wrong.' * Here 
he anticipates Helmholtz. 

The researches of Joule were final and conclusive. 
Extending over a period of several years, probably 
originating before 1840 (the first paper appeared in 
that year), they are models of skilful experiment and 
accurate induction. They were concluded in 1849, 
when the dynamical equivalence of heat was finally 
established. This led to the enunciation of the first 
law of thermo-dynamics, that c when equal quantities 
of mechanical effect are produced by any means what- 
ever from purely thermal sources, or lost in purely 
thermal effects, then equal quantities of heat are put 
out of existence or are generated ; and for every unit 
of heat measured by the raising of a pound of water, 
i Fahrenheit in temperature, you have to expend 
772 foot-pounds of work.' The principle was estab- 
lished by Joule for mechanical work, current electricity, 
electro - magnetism and light. Thus the grandest 
generalisation of physical science the conservation of 
energy is founded on the mechanical theory of heat. 2 

1 Colding, Phil. Mag., Jan. 1864. 

- Tail, Recent Advances, op. cit., p. 64. 



The first in Great Britain to recognise the immense 
importance of the principle was William Thomson, 
now Lord Kelvin, who applied it with such force to 
thermo-dynamics as to practically create this depart- 
ment of science. He also formulated the comple- 
mentary doctrine of the dissipation of energy. 

It has been necessary to give this slight sketch of 
the development of these great ideas so as to enable 
one to estimate with some degree of accuracy how 
much was contributed by Helmholtz. He approached 
the subject from the purely mathematical point of 
view. With the writings of Newton, Leibnitz, 
Descartes and d'Alembert in the field of his mental 
vision, he starts by making two assumptions. The 
first is as follows : Suppose matter to ' consist of 
ultimate particles which exert on each other forces 
whose directions are those of the lines joining each 
pair of particles, and whose amounts depend simply on 
the distance between the particles ; suppose, in fact, 
that something akin to gravitation force exists amongst 
all the particles of matter in the universe, that each 
particle attracts every other particle with a force 
which depends only on the distance between them, 
not in any way upon the sides which are turned to 
one another, so that if you know the distance between 
them you know the amount of the attraction, and that 
the attraction shall also be (in accordance with 
Newton's Third Law of Motion) in the direction 
of the line joining them. If that assumption is made, 


then it is a consequence of the laws of motion of 
gross matter that if all the forms of energy depend 
upon motion or position of particles, the conservation 
of energy must hold, and also that the so-called 
perpetual motion would be impossible under any 

As an alternative, Helmholtz reasoned in the 
following manner : Assume the impossibility of the 
so-called perpetual motion, and consider also Newton's 
second interpretation or explanation of the Third 
Law of Motion, then these two thoughts would 
by themselves lead to the proof of the principle of 
the conservation of energy. But the perpetual 
motion has been demonstrated by experiment to be 
impossible. This being an experimental fact, and 
Newton's statement being also universally true, the 
principle of the conservation of energy is established. 
Thus Helmholtz, by a purely theoretical considera- 
tion of the matter, made the great discovery for 
himself. It is no detraction to the work of Helm- 
holtz on this subject that it was theoretical. One 
of the main objects of theoretical research is to find 
the point of view in which the subject appears in 
its greatest simplicity. It is also its purpose to give 
the form in which the results of experiments may 
be expressed. Theory leads to the conception of 
functions the forms of which must be settled by 

As already mentioned, the application of the prin- 


ciple of the conservation of energy to living beings 
was first clearly made by Robert Mayer. Nothing 
will give a better notion of this line of thought than 
the following quotation from Mayer's well-known 
paper on 'Organic Motion and Nutrition':- 

' The second question refers to the cause of the 
chemical tension produced in the plant. This ten- 
sion is a physical force. It is equivalent to the heat 
obtained from the combustion of the plant. Does 
this force, then, come from the vital processes, and 
without the expenditure of some other form of force ? 
The creation of a physical force, of itself hardly 
thinkable, seems all the more paradoxical when we 
consider that it is only by the help of the sun's rays 
that plants perform their work. By the assumption 
of such a hypothetical action of the "vital force," 
all further investigation is cut off, and the application 
of the methods of exact science to the phenomena 
of vitality is rendered impossible. Those who hold 
a notion so opposed to the spirit of science would 
be thereby carried into the chaos of unbridled phan- 
tasy. I therefore hope that I may reckon on the 
reader's assent when I state, as an axiomatic truth, 
that during vital processes a conversion only of matter^ 
as well as of force, occurs^ and that creation of either the 
one or the other never takes place. 

'The physical force collected by plants becomes 
the property of another class of creatures of animals. 
The living animal consumes combustible substances 


belonging to the vegetable world, and causes them to 
reunite with the oxygen of the atmosphere. Parallel 
to this process runs the work done by animals. This 
work is the aim and end of animal existence. Plants 
certainly produce mechanical effects, but it is evident 
that for equal masses and times the sum of the effects 
produced by a plant is vanishingly small compared 
with those produced by an animal. While, then, in 
the plant the production of mechanical effects plays 
quite a subordinate part, the conversion of chemical 
tensions into useful mechanical effect is the character- 
istic sign of animal life. In the animal body chemical 
forces are perpetually expended. Ternary and qua- 
ternary compounds undergo, during the life of the 
animal, the most important changes, and are, for the 
most part, given off in the form of binary compounds, 
as burnt substances. The magnitude of these forces, 
with reference to the heat developed in these processes, 
is by no means determined with sufficient accuracy ; 
but here, where our object is simply the establishment 
of a principle, it will be sufficient to take into account 
the heat of combustion of the pure carbon. When 
additional data have been obtained, it will be easy 
to modify our numerical calculations so as to render 
them accordant with the new facts.' 

(He then goes on with calculations.) 

' If the animal organism applied the disposable com- 
bustible material solely to the performance of work, 
the quantities of carbon just calculated would suffice 


for the times mentioned. In reality, however, besides 
the production of mechanical effects, there is in the 
animal body a continuous generation of heat. The 
chemical force contained in the food and inspired 
oxygen is therefore the source of two other forms of 
power, namely, mechanical motion and heat ; and the 
sum of these physical forces produced by an animal is 
the equivalent of the contemporaneous chemical process. 
Let the quantity of mechanical work performed by an 
animal in a given time be collected and converted by 
friction or some other means into heat ; add to this 
the heat generated immediately in the animal body at 
the same time, we have then the exact quantity of 
heat corresponding to the chemical processes that have 
taken place. 

c In the active animal the chemical changes are 
much greater than in the resting one. Let the 
amount of the chemical processes accomplished in a 
certain time in the resting animal be x y and in the 
active one be x +y. If during activity the same 
quantity of heat were generated as during rest, the 
additional chemical force y would correspond to the 
work performed. In general, however, more heat is 
produced in the active organism than in the resting 
one. During work, therefore, we shall have x plus a 
portion of y heat, the residue of y being converted into 
mechanical effect. 

4 The maximum mechanical effect produced by a 
working mammal hardly amounts to one-fifth of the 


force derivable from the total quantity of carbon con- 
sumed. The remaining four-fifths are devoted to the 
generation of heat.' 

It will be seen that the doctrine of the conservation 
of energy was of the highest importance in physiology, 
as it indicated the road to a thorough investigation of 
the nutritional changes occurring in living matter. 
These nutritional changes, if in the direction of the 
upbuilding of tissues, are also concerned in the storing 
up of energy, and if, on the contrary, they are asso- 
ciated with the tearing down of tissue, or, in other 
words, with chemical decompositions, then energy is 
set free as mechanical motion, heat, light or elec- 
tricity. The doctrine also appeared to its early 
teachers, at all events, fatal to any vitalistic theory. 
Time, however, has shown that there still are pheno- 
mena connected with living matter that are outside 
the range of even this great principle, such as the facts 
of consciousness. 




IN 1849, in his twenty-ninth year, Helmholtz was 
appointed to the Chair of Physiology and General 
Pathology in the University of Konigsberg. Here 
he spent six busy years, fully engaged in teaching 
and investigation. In the year of his removal, 1849, 
no contributions appeared, and we can readily believe 
the youthful professor was establishing himself in his 
new sphere of duty. 

Early in this year, also, he married Miss Olga 
Von Velten, of Potsdam, who died soon after his 
settlement in Heidelberg in 1859. Two children 
were born of this marriage a daughter, who became 
the wife of Professor Branco, a well-known geologist, 
and a son, who is an engineer in Munich, still sur- 
vives. Helmholtz loved a quiet home life, with the 
pleasures of congenial society and music, to which he 
was devoted. He was an accomplished pianist, and 
he sang a little, but his voice was not strong. As 
his days were devoted to scientific labour, and as he 


shunned publicity for the greater part of his life, there 
is little of incident to relate. 

The stream of original papers began to flow in 
1850, and it increased in volume until he moved to 
Bonn in 1856. One is astonished at the number of 
researches of first-rate importance. Helmholtz did 
not, like many, lose time in doing second-rate work 
that others, perhaps, could have done better. His 
scientific instinct appeared to guide him often into 
what are termed virgin fields. Thus he had the 
great satisfaction of collecting the first fruits, and he 
usually gathered so well as to leave little for others 
who came after him. Hence the researches and dis- 
coveries that were announced in rapid succession were 
always epoch making, and always in a special sense 
his own. During this period he measured the rate 
of the nervous impulse, he invented the ophthalmo- 
scope, and he began those investigations on colour 
and sound that will for ever be associated with his 

The measurement of the rate of the nervous im- 
pulse was accomplished in 1850. The problem was 
to measure the rate at which the nervous impulse 
travels along a sensory nerve, say from the tip of the 
finger to the brain, or along a motor nerve, say from 
the brain to one of the muscles of the arm. When 
we touch the finger, no time seems to elapse between 
the moment of touching and the moment when we 
are conscious of having touched something. When 


we will to move the forefinger, the commands of the 
will appear to be instantaneously carried into effect. 
This arises, however, from our limited appreciation 
of shorter intervals of time than say the one-tenth of 
a second, so that if less time elapsed between the 
moment of touching the finger and the moment of 
the sensation, the two events appear to be one. It 
was necessary, therefore, to have some means of re- 
cording the duration of short periods of time, such 
as the short period assumed to exist between the 
moment of irritating a nerve and the moment of 
the contraction of the muscle supplied by it. 

Manifestly the subject could be investigated most 
easily by using the muscle of the frog and the motor 
nerve passing to it. Helmholtz made use of the 
graphic method of recording the contraction of 
muscle, already invented by him in the form of the 
well-known myograph. Just about this time elec- 
trical mechanisms had been introduced into practical 
physiology by Du Bois Reymond, and Helmholtz 
made good use of these appliances. He first em- 
ployed, as a means of recording the beginning and the 
end of the phenomenon, a method devised by Pouillet, 
which consisted in noting the instant of the move- 
ment of the needle of a galvanometer when an in- 
stantaneous current was sent through the instrument, 
taking it for granted that the duration of the current 
itself was practically nothing. Suppose, then, that an 
arrangement was made by which a nerve could be 


irritated, say at a distance of two inches from the 
muscle, by an electric current, which also moment- 
arily passed through the galvanometer, the move- 
ment of the needle would indicate the instant when 
the nerve was stimulated. Helmholtz, in the first 
place, improved Pouillet's method by causing the 
opening or closing shock from an induction coil to 
irritate the nerve, either near to the muscle or far 
from it, and he so arranged the experiment that 
at the moment of opening the induction current, 
the galvanometer circuit was closed, and was again 
opened by the contraction of the muscle itself. The 
interval, then, between the two swings of the needle 
was that between the moment of irritating the nerve 
and the moment of the muscular contraction. Ar- 
rangements were then made for irritating the nerve 
in two successive experiments first, close to the 
muscle, and, second, at a distance of say two inches 
from it. It was soon found that the muscle did not 
respond at the instant the stimulus was applied to 
the nerve, and that the further away the nerve was 
irritated the later was the response. The first dis- 
covery was that even when the nerve was irritated 
close to the muscle, a period of something like the 
TTjijth of a second always elapsed before the muscle 
began to contract. In other words, the muscle did 
not at once respond, but some time was occupied 
in those molecular changes that precede contraction. 
This period was termed by Helmholtz the period of 


latent stimulation. Edward Weber had endeavoured 
to draw a distinction between the movements of in- 
organic and animal matter by assuming that the latter 
were instantaneous, but the discovery of the latent 
period at once put this distinction out of the question. 
Helmholtz next made use of the graphic method, 
introduced about that time into physiological investi- 
gation, and the muscle, by means of a myograph, was 
caused to write the curve of its contraction on the 
blackened surface of a rotating drum. About the 
beginning of the century, Thomas Young showed 
how time might be recorded by marks made on a 
rotating cylinder, moving with a uniform velocity. 
James Watt then applied the graphic method to 
recording the movements of the indicator of his 
engine on a cylinder rotated by the engine itself. 
Thus he obtained a curve representing variations 
of steam pressure at different times. This suggested 
to Ludwig, then at the beginning of his important 
investigations into the dynamics of the circulation, 
the conception of the kymograph, by which varia- 
tions of pressure in the blood vessels of a living animal 
were recorded on a drum in a series of waves, the 
smaller ones corresponding to the individual beats of 
the heart, and the larger to the respiratory move- 
ments. The myograph of Helmholtz, already re- 
ferred to (p. 36), recorded the shortening of the 
muscle with great exactitude, and thus Pouillet's 
galvanometrical method was discarded. He con- 


structed a special myographion, in which a weight, 
by centrifugal action, liberated a spring that set 
free a simple mechanism by which a current pass- 
ing through the primary coil of a small induction 
machine was opened. The shock thus obtained from 
the secondary coil passed instantaneously to the nerve, 
the nervous impulse was generated at the point irri- 
tated, the impulse then travelled down the nerve, 
and the muscle contracted, writing its curve on the 
rotating drum. In this way two curves were traced 
on the cylinder, one by contraction of the muscle 
when the nerve was stimulated close to the muscle, 
and the other when it was stimulated at a distance 
from it. As the nerve, whether stimulated near or 
far from the muscle, always received the induction 
shock at the same moment when the cylinder had 
attained its maximum velocity, the two curves did 
not coincide at their commencement, the one corre- 
sponding to the experiment in which the nerve 
was stimulated at a distance being a little behind 
the one produced when the nerve was stimulated 
near the muscle. Thus during the time that 
the nervous impulse was travelling, say along two 
inches of nerve, the cylinder had travelled a short 
distance farther on that is to say, had rotated round 
its axis. The distance between the beginnings of 
the two curves expressed the time occupied by the 
nervous impulse in passing along a given length of 
nerve. If the velocity of the cylinder had been 


determined, then this distance represented a certain 
period of time. 

By this method a single experiment gave results 
that could only have been obtained, with much 
trouble and possibilities of inaccuracy, by a whole 
series of observations by Pouillet's method. The ex- 
periments showed that in the motor nerves of the 
frog the velocity of the nervous impulse was only 
about ninety feet per second (that of a very quick 
express train), or about y^th part of the velocity of 
sound in air, a result quite unexpected. Until the 
question was submitted by Helmholtz to the test of 
experiment, the wildest conjectures had been indulged 
in by speculative physiologists. Thus the iatro- 
mathematicians of Montpellier said that the rapidity 
bore a ratio to that of the blood in the aorta, namely, 
in the proportion of the diameter of the aorta to that 
of a nerve fibre, a statement that implied a velocity 
of the nervous impulse 600 times more rapid than 
light ! Haller took as the basis of his conjectures 
the number of vibrations made by the tongue in pro- 
nouncing the letter R, and, by a series of deductions, 
most of them wide of the mark, he strangely arrived 
at a conclusion not very far ofF what we know to 
be correct, namely, that the velocity was about 150 
feet per second. 1 Johannes Miiller despaired of being 

1 Haller's Elementa, t. iv., p. 372 ' Ego vero, cum haec mere theoretica 
sint experimento uti malim, etsi minor summa prodit. Ita invenio 
sum ma in tamen celeritatem esse muscular is liquid i ut non minus quam 
9000 pedes in minuto percurrat.' 

6 4 


able to solve the problem, chiefly because of the short- 
ness of the nervous tracts in the living animal, and 
although he doubted the results given by the older 
physiologists, he thought that the velocity of the 
nervous impulse must be akin to that of light. In 
his great text-book he makes use of the phrase, 
c Such immeasurable rapidity.' Again, he says, 
' We shall probably never attain the power of meas- 
uring the velocity of nervous action, for we have 
no opportunity of comparing its propagation through 
immense space as we have in the case of light.' I 
Such was the state of opinion when Helmholtz took 
up the subject. His versatile intellect suggested the 
method by which the problem could be attacked 
through the nerves and muscles of a frog, and, as 
one writer remarks, * he apparently felt as much at 
home with frogs' nerves and muscles, and with 
intervals of time of thousands of a second, as he was 
in after years in discussing the universe and the 
immense measurements of time and space involved 
in a consideration of the planets.' 

As already mentioned, Du Bois Reymond was 
about the same period engaged on his researches on 
animal electricity. Following Matteucci, but with 
much finer apparatus and with clearer ideas, he had 
shown, by means of the galvanometer, and specially- 
constructed non-polarisable electrodes, that the trans- 
verse section of a resting muscle is negative to the 

1 Muller's Physiology, trans, by Baly, vol. i., p. 678. 


surface, as indicated by the movement of the needle 
of the galvanometer in a certain direction. This was 
termed the resting current. If, then, the muscle is 
caused to contract, there occurs what Du Bois Reymond 
called * the negative variation,' that is to say, the needle 
gave ; a swing towards zero, or even crossed to the other 
side. This negative variation, now called 'the action 
current,' is an electrical phenomenon connected with 
the activity of the muscle, and the electric change 
is of sufficient intensity to irritate the nerve of a 
muscle preparation, as shown in Matteucci's famous 
experiment, usually called the ' induced contraction.' 
In this experiment the nerve of a muscle, a y is 
stretched over a muscle , and if the nerve of b is 
irritated by an electric shock, not only b but also a 
is thrown into contraction, because the c negative 
variation ' in muscle b irritates the nerve of muscle a. 
Helmholtz attacked the time relations of this problem, 
and he thought he could demonstrate that the nega- 
tive variation occurred only in the period of latent 
stimulation, and that it was over and gone before the 
muscle began to contract. All this work related to 
motor nerves and to the muscles and nerves of the 

It seemed a more difficult problem to determine the 
velocity in sensory nerves. When we touch a sensory 
nerve, the message goes to the brain, but how could 
it be possible to estimate the time it occupies in going 
that distance, seeing the brain can only respond by a 


muscular act r Helmholtz devised a method by which 
what is called the ' reaction period ' may be computed, 
that is the time between the moment of stimulating, 
say the skin of the foot and the moment the indi- 
vidual makes a signal that he has felt the sensation. 
The reasoning is as follows : Suppose a sensory nerve 
to be excited in the hand, the theory of nervous con- 
duction is that a change is propagated along the nerve 
to the brain, and that in the brain the molecular 
changes occur which result in a sensation. The 
individual having the sensation may feel it and make 
no sign by which anyone else might be made aware 
that he has felt it, or the subject of the sensation 
might, by a muscular movement, such as the motion 
of an arm, let anyone else see that he has felt the 
sensation. We have no means of knowing whether 
or not an individual has felt a sensation except by the 
individual making some kind of gesture or muscular 
movement. Now, it is clear that, if we regard the 
brain as the seat of the changes resulting in sensation, 
the nearer any stimulated portion of skin is to the 
brain the sooner will the brain feel and respond to 
the stimulus. Thus, if the skin on the big toe of 
the right foot be stimulated, the effect of the stimulus 
will pass to the brain and there call forth a sensation ; 
but if the stimulus be applied to the skin at the top 
of the thigh, it is evident the effect will have to pass 
along a shorter length of nerve, and that the sensation 
in the brain will be aroused sooner. If we suppose 


that in each case the individual who is the subject of 
the experiment indicates the moment he feels the 
sensation, and that the instant the stimulus is applied 
successively to the skin on the toe and on the thigh 
is also accurately recorded, it is clear that he will 
signal the sensation of stimulation of the toe a little 
later than when he signals stimulation of the skin on 
the thigh, and that the difference will indicate the 
time required by the change in the nerve to pass 
along the length of the nerve from the toe to the 
thigh. In the observation it is assumed that the time 
required for the changes in the brain, resulting in sen- 
sation and volition, for the transmission along the 
motor nerve, and for the muscular contraction re- 
quired to signal, is the same in each experiment. 
Thus, supposing the total time between the moment 
of stimulating and the moment when the signal that 
the sensation has been felt and responded to be *, it 
is clear that this time is composed of <z, the time 
required for the passage of the nerve current in the 
first experiment from the toe to the brain ; of , the 
time required for the changes in the brain involved in 
sensation and volition ; and of c y the time required for 
the transmission along the motor nerves and for the 
muscular contraction to move the signal that is, 
x = a + b + c. But if the time between the moment of 
stimulating the thigh to the moment of signalling be 
shorter, and supposing that b and c are constant, then 
a will vary according to the length of the nerve. 


Suppose the difference of time between the registra- 
tion of stimulating at the toe and at the thigh to 
be y, then in the second experiment x = a-y + b + c; 
that is, y = the time occupied by the passage of the 
nerve current from the toe to the thigh. By this 
method the velocity of the nervous impulse in the 
sensory nerves in man is found to vary from 50 to 100 
metres per second (160 to 300 feet). 

It will be noted that for motor nerves the obser- 
vations were made on the frog and for sensory nerves 
on man. The next question Helmholtz solved was : 
Is the velocity the same or different in the two kinds 
of nerves ? By attaching the thumb to a myograph 
and then stimulating near the wrist and at the elbow, 
it was found that the muscles of the thumb contracted 
a little later after stimulation at the elbow ; that is to 
say, the nervous impulse took some time in travelling 
from the elbow to the wrist. Two curves were 
obtained practically by the same method as was used 
in determining the rate in the motor nerve in the 
frog, and the velocity was found to be the same as 
in the sensory nerves of man. In both kinds of 
nerves, cold was found to retard and heat to acceler- 
ate the velocity of transmission. 

These important observations not only threw light 
on the question of the transmission of the nervous 
impulse, but they prepared the way for the determina- 
tion of time relations in many nervous processes. 
Astronomers had long known that in watching and 


signalling the moment of the transit of a star, there 
were slight differences in the observations made by 
equally competent observers, differences apparently 
due to individuality. It is said that Maskelyne dis- 
missed an assistant because, in making observations, 
he was always behind his master in point of time. 
Bessel was the first to recognise that the discrepancies 
were due to the fact that men feel and even think at 
different rates. As Hermann points out, the coinci- 
dence is striking that years afterwards, in the very 
university where Bessel worked, Helmholtz showed 
that there was a physiological basis for his conjecture. 
Psycho-physical investigators of later times, with im- 
proved appliances, have measured the time occupied 
in reflex actions, and even in those psychical operations 
involved in choice, discrimination and volition. Many 
ingenious instruments have since been devised, but 
the root idea of them all may be traced back to those 
experiments of Helmholtz, which originated the 
methods of the psycho-physical school of investigators. 




IN 1851 Helmholtz conferred an inestimable benefit 
01 humanity, became famous far beyond the 
circle :>f his scientific friends, and handed his name 
on to posterity by the invention of the ophthalmo- 
scope. Had he done little else in his long lifetime, his 
name would never be forgotten ; and yet the inven- 
tion cf this instrument took its origin not in any 
profound investigation, but in the desire to exhibit 
a physiological phenomenon to his students. It was 
chara:teristic, however, of his mind that he was ever 
recepive of new impressions, and when an idea 
occured to him, his powers were brought persistently 
to be;r upon it, and if it involved a problem, he had 
no nst until it was solved. The invention of the 
ophthalmoscope is a striking example, also, of his 
singular power of combining the theoretical with the 
practcal in his daily life ; and he could turn his mind 
from the contemplation of the mathematical expres- 
sions of the law of the conservation of energy, trac- 
ing m his imagination its tremendous consequences, 
to cevising the best method of illuminating the eye. 
7 1 


At the same time, although he was practical, no one 
more strongly denounced the pursuit of science 
merely for its practical results. All his physiological 
work, whilst of the most thorough-going kind, was 
pursued because it was his duty as a disciple of 
science to ascertain the truth, and he felt sure that 
any practical advantage to medicine, or to science 
in general, would naturally flow from what to many 
would seem to be abstruse and theoretical work. He 
did not require to invent an ophthalmoscope to show 
the practical side of his genius ; it was the outcome 
of his knowledge of science, including the aratomi- 
cal structure of the eye and the laws of optics Yet 
the invention of this little instrument, fron the 
time of its conception the daily companion of medical 
men all over the world an instrument, too, that can 
scarcely be supplanted by any other will keep his 
memory green when many of his more elaborate 
works may be forgotten, or are absorbed in the general 
body of scientific truth. 

In a speech, delivered many years after, Helrrholtz 
remarked, 'In Konigsberg I had to teach gmeral 
pathology and physiology. A teacher in a university 
is subject to excellent discipline, in that he is oUiged 
each year not only to give at least an outline o" the 
whole of his science, but also to convince and s;tisfy 
the clear heads among his hearers, some of whom 
will be the great men of the next generation. This 
necessity was most beneficial to myself. In prorar- 


ing my lectures, I was led to devise the method of 
measuring the velocity of the nervous impulse, and 
also to the conception of the ophthalmoscope. This 
instrument became the most popular of my scientific 
achievements ; but I have already pointed to the 
oculists how much good fortune, rather than any 
personal merit, favoured me in its invention. I was 
endeavouring to explain to my pupils the emission of 
reflected light from the eye, a discovery made by 
Briicke, who would have invented the ophthalmo- 
scope had he only asked himself how an optical 
image is formed by the light returning from the 
eye. In his research it was not necessary to ask 
it, but had he asked it, he was just the man to 
answer it as quickly as I did, and to invent the 
instrument. I turned the problem over and over to 
ascertain the simplest way in which I could demon- 
strate the phenomenon to my students. It was also 
a reminiscence of my days of medical study, that 
ophthalmologists had great trouble in dealing with 
certain cases of eye disease, then known as black 
cataract. The first model was constructed of paste- 
board, eye lenses, and cover glasses used in the micro- 
scopic work. It was at first so difficult to use, that 
I doubt if I should have persevered, unless I had felt 
that it must succeed ; but in eight days I had the 
great joy of being the first who saw before him a 
living human retina.' 

It had long been known that the eyes of certain 


animals, more especially those of birds of prey, 
glisten or sparkle in the dark. If a cat is observed 
entering a room in shadow, her eyes may be seen 
like little balls of fire, and the red eyes of white rabbits 
and other albinos are familiar to everyone. In 1811, 
Pallas suggested that perhaps one saw in such cases the 
naked electricity of the retina (forte nudum electrlcum 
retina nervte}. Johannes Miiller proved the truth of 
the view first suggested by Hassenstein, that such eyes 
do not really emit, but only reflect light, and it 
was found that those eyes glistened most which were 
furnished with a special structure, called a tapetum, 
adapted for the reflection of light. Briicke was the 
first to show that all eyes could be made to glisten by 
throwing into the eye the beam of a lantern while 
the rest of the room was dark ; and it is said that at 
night he went to the Zoological Gardens and found 
that, by taking up a suitable position, he could 
illuminate the eyes of all animals. He then tried 
the experiment with the human eye, guided by the 
curious bit of information, that a servant of his father 
had been dismissed from his situation because it was 
* uncanny ' to see his eyes shining in the dark ! 
The first eyes that were illuminated by Briicke, so 
as to cause them to shine, were those of his friend 
Du Bois Reymond. Soon afterwards von Erlach, 
of Bern, who happened to wear concave spectacles, 
found that by placing his glasses at a particular angle, 
and thus reflecting light into the eyes of his patient, 


he could make them shine, an experiment very easily 
repeated. Then came Helmholtz, who went deeper 
into the subject, and invented the instrument. It 
will be seen how true it was that Briicke came near 
the invention, but still there is all the difference in 
the world between doing a thing and not doing it. 
The first account of the ophthalmoscope was pub- 
lished in 1 85 1. 1 

In his great work on physiological optics, the first 
part of which was published in 1856, Helmholtz 
gives a full account of the whole subject, and as it is 
of extreme interest to medical men, I shall take the 
liberty of making full use or it, sometimes using his 
own words. 

Light from the eye has been observed from early 
times coming from the eyes of dogs, cats and other 
animals who had a tapetum in the fundus of the eye 
that is to say, an area devoid of pigment, and covered 
with thin and highly-reflecting fibres. In these animals 
the reflection is so intense as to be easily perceived, 
even in unfavourable circumstances. The ancient 
and prevalent opinion was that those luminous eyes 
developed light, and that when the animals were 
irritated, light was evolved from their eyes under the 
influence of their nervous system. As the light of 
the eyes is best recognised when the light comes 
from behind the observer and skims over his head, it 

1 Beschreibung etna Augenspugch zur Untersuchung der Nerzhaut m 
lebtnden Auge. Berlin, 1851. 



is easy to understand that a source of light so placed 
had escaped all observers. It was also held that the 
eyes of white rabbits and of albinos had a light 
of their own. Prevost, in 1810, was the first to show 
that the light of the eyes of animals was never seen 
in complete darkness, that neither an effort of will 
nor irritation caused it, and that it was always due 
to the reflection of an incident light. Gruithuisen 
found the same result, and further showed that the 
cause of the phenomenon was in the tapetum along 
with the ' refraction extraordinaire ' of the lens. He 
also saw the light in the eyes of dead animals. These 
facts were confirmed by Rudolphi, Johannes Miiller, 
Esser, Wiedemann and Hassenstein. Rudolphi ob- 
served that we must look at the eye in a certain 
direction to perceive the light ; and Esser gave a 
good explanation of the changes of colour by the 
appearance of different coloured parts of the retina 
which were presented successively behind the pupil. 
Hassenstein, finally, found that light was produced 
when the eye was compressed along its axis, and 
supposed that in the living animal luminosity might 
be produced voluntarily by a shortening of the axis by 
pressure of muscles. The earlier observers recognised, 
then, luminosity of the eye as a phenomenon of re- 
flection without giving an account of the conditions 
that determined it. 

In the human eye luminosity was observed in 
certain rare diseases, in particular when tumours occu- 


pied the fundus of the eye. Behr, in 1839, met 
with a case in which the iris was absent, in which 
there was luminosity, and noted that the eyes of 
the observer must regard those of the patient in a 
direction nearly parallel to that of the incident rays ; 
such was also the basis of Briicke's method of observ- 
ing the ocular light. In the case of absence of the 
iris, the luminosity was not marked when the retina 
was strongly illuminated. Accommodation was im- 
perfect in such a case. 

Finally W. Gumming 1 and Briicke, in 1847, found, 
independently of each other, the method of rendering 
the normal human eye luminous, when the observer 
looks at it in a direction nearly parallel to the incident 
rays. Briicke had already applied his method to the 
eyes of animals furnished with a tapetum. At last, 
Wharton Jones, in 1854, writes that Charles Babbage 
had shown to him, about the same time, a silvered 
mirror from which a small portion of the foil had been 
removed, by which light could be thrown into the eye, 
and at the same time the observer could look at it 
through the opening. This description applies well to 
the ophthalmoscope of Coccius, but as Babbage does 
not appear to have used lenses with his mirror, he 
could not, in the opinion of Helmholtz, clearly see 
the retina, and probably, for that reason, he did not 
publish the discovery. It is evident, however, that 
Babbage almost invented the ophthalmoscope. 

1 Medico-Chirurgical Trans., vol. xxix., p. 284. 



The other aspect of the question, why the parts of 
the retina, even when illuminated, as in the eyes of 
animals having a tapetum, and, in albinos, could not 
be distinguished, has been made the subject of much 
discussion. The solution was easy. In the beginning 
of the eighteenth century, Mery (1704) had observed 
that he could see the vessels of the retina of a cat 
immersed in water, the eyes of which were strongly 
luminous. La Hire, in 1709, gave a correct explana- 
tion of this phenomenon. He said that it was due to 
a change in the refraction of the rays that made the 
eye luminous, but he did not attempt to give a more 
precise explanation. It was the same with Kussmaul 
in 1845. He showed that the retina became clear 
and recognisable when the cornea and the crystallin 
were removed, or when a small portion of the 
vitreous was removed, thus shortening the axis of 
the eye. 

Helmholtz was the first to give a complete account 
of the relation existing between the directions of the 
incident and emergent rays, and he gave the true 
explanation of the blackness of the pupil. He em- 
ployed for illumination, plane unsilvered glasses, and, 
to see the retina better, concave lenses. H. Reute 
(in 1852), on the other hand, was the first to use a 
mirror having a hole in the centre, and convex glasses. 
As the new instrument soon acquired great importance 
in ophthalmology, many ophthalmoscopes of different 
forms have been made, but they do not involve any 


essentially new method for illuminating and examining 
the retina. 

Of the light which strikes on the retina, one part is 
absorbed, and that principally by the black pigment of 
the choroid, and the other part is diffusely reflected, 
and returns from the eye through the pupil. In ordin- 
ary circumstances, we do not perceive the light which 
issues from the pupil ; this opening, on the contrary, 
appears jet black. We must look for the explanation 
in the particular conditions of refraction in the eye, 
and we must also remember that, owing to the pig- 
mentation of the eye, only a small amount of light is 
returned from it. In all systems of refractive surfaces 
(lenses), which form an image of a luminous point, 
the rays may be traced from the image to the lumin- 
ous point, traversing exactly the same path as they 
followed in passingfrom the luminous point totheimage. 
In other words, if we put the luminous point in the 
position first occupied by the image, the image will 
now be formed in the place previously occupied by the 
luminous point. 

The result is as follows : When the human eye is 
exactly accommodated for a luminous point, and forms 
an exact image of the point on the retina, if we con- 
sider the illuminated part of the retina as a second 
luminous object, the image formed by the media of the 
eye coincides exactly with the body given ; so, in 
front of the eye, all the light which returns from the 
retina is directed towards the luminous body, and it 


does not pass by the side of this body. To receive a 
part of this light, it is necessary that the eye of the 
observer be placed between the luminous body and the 
illuminated eye ; this evidently cannot be done with- 
out intercepting the light which goes to the illumin- 
ated eye, unless we employ a special device. An 
observer, moreover, cannot see the light returned from 
one eye into the other if the last is exactly accommo- 
dated for the pupil of the observer. In these circum- 
stances, there is formed on the retina of the eye observed 
an exact but dim image of the pupil of the observer. 
Conversely, the media of the eye under observation 
forms precisely on the pupil of the observer an exact 
image of its retinal image, and, consequently, the 
observer can only see in the eye of the other the 
reflection of his own black pupil. This explains how, 
in ordinary circumstances, we cannot see the fundus 
of the eye we look at, and how we cannot distinguish 
even the parts which reflect the light the most strongly, 
such as the point of entrance, generally white, of the 
optic nerve or the blood vessels. The pupil appears 
black even in albinos (subjects in whom the choroid 
has no pigment), if we take the precaution to inter- 
pose a black card, having a hole in it the diameter 
of the pupil, and thus prevent the light from 
penetrating into the eye through the sclerotic, an 
observation first made by Donders. It is, in reality, 
the light which passes through the sclerotic which 
gives to the pupil of albinos its well-known red colour. 


In the same way the objective of a camera appears 
black in a dark room when we throw on it the 
image of a single flame. If the eye observed is, 
on the contrary, neither exactly accommodated for 
the luminous body, nor for the pupil of the observer, 
it is possible that we may perceive a little of the light 
which emerges from the observed eye, and the pupil 
may then appear to be luminous. It is easy to see 
that the observer may receive light coming from all 
points of the retina of the eye under observation, on 
which falls the diffusive image of his own pupil. If 
we substitute a luminous disc for the pupil of the 
observer, the image of diffusion formed of this disc 
in the eye observed will coincide exactly with that of 
the pupil of the observer, for luminous rays will radiate 
from one or many points of the disc to each point of 
its image of diffusion ; then, conversely, the rays given 
off from each point of the circle of diffusion will reach 
one or many points of the luminous disc, that is to 
say, the pupil of the observer. The eye observed 
appears luminous when the image of diffusion of the 
pupil of the observer coincides with that of a luminous 
object in the eye observed. If then we look at an 
eye by a light from a flame from which we have shut 
off, by an opaque screen, the rays that dazzle us, 
whether the eye observed is accommodated for a distant 
or near object, its pupil will appear illuminated in red. 
During the experiment accommodation must be 
at rest, if the observer is far away, because the 



least inexactitude of refraction or of accommodation 
will allow some of the rays to reach the observer, and 
we are most likely to succeed if the subject of observa- 
tion looks to the side. The illumination is most 
brilliant when the incident light falls on the place of 
entrance of the optic nerve, because the white sub- 
stance of the papilla reflects light strongly, and be- 
cause, on account of its diaphanous structure, the 
surface is not so uniform as to receive a perfectly sharp 

Thus it will be seen that the invention of the 
ophthalmoscope was not a happy guess, but was the 
outcome of a careful sifting of the facts of vision. 
In this invention, and in its theoretical explanation, we 
have an excellent example of Helmholtz's thorough- 
ness. In many of its arrangements the ophthal- 
moscope has been made more easy to use, and the 
observation of the inverted image has its advantages, 
but we have it on the authority of Donders and 
von Jaeger, that the instrument in its original form 
is optically complete. Helmholtz also saw how the 
instrument could be serviceable to ophthalmologists, 
not only as regards the examination of the fundus and 
the observation of changes in the retina, but also as to 
how the refractive conditions can be accurately esti- 
mated. In this way, the degrees of myopia (short- 
sightedness), hypermetropia (far-sightedness), and of 
that peculiar condition known as astigmatism (in 
which the meridians of curvature of the refractive 


structures, the cornea and lens, are not the same), may 
all be determined. The invention of the instrument 
was a new era, not only for ophthalmology, but also 
for practical medicine, as the retina may be regarded 
as an outlying portion of the brain ; an examination 
of the fundus of the eye often gives the physician 
information as to pathological changes occurring in 
the nerve centres. Thus it is of service in the diag- 
nosis of inflammatory actions in the brain, both acute 
and chronic ; of changes in the meninges, or brain 
coverings ; in locomotor ataxia ; in the various forms 
of Bright's disease ; and many other maladies. 

The retina presents to the observing eye the ap- 
pearance of a red-coloured concave disc with a whitish 
oval spot to the inner side, where the optic nerve 
enters, from which we see branching the retinal 
vessels, the veins being darker in colour than the 
arteries, and in the visual axis lies the yellow spot, 
which is the most sensitive part of the retina. The 
vessels of the fovea centralis, a minute depression in 
the centre of the yellow spot, are so fine as to be 
invisible to the naked eye. 

When von Graefe first saw the fundus of the living 
human eye, with its optic disc and blood vessels, his face 
flushed with excitement, and he cried, ' Helmholtz has 
unfolded to us a new world ! What remains to be dis- 
covered ? ' Before the invention of the ophthalmoscope, 
diseases of the fundus, and even disturbances of refrac- 
tion and accommodation of the most diverse character 


were not differentiated, and the same treatment was 
applied to all alike, often with disastrous results to 
the patient. In an eloquent speech by von Graefe, 
delivered at Heidelberg in 1858, on the occasion of the 
Ophthalmological Congress, he said, l Under our eyes 
we see the mists disperse, which, for hundreds of 
years, have clouded the view of our best observers, 
and an unexampled field is won for the healing art, 
from which, even already, after a few brief years, 
have been reaped most admirable fruits.' Then, 
turning to Helmholtz, he handed him, in the name 
of the Congress, a cup, on which were inscribed the 
words : * To the creator of a new science, to the 
benefactor of mankind, in thankful remembrance of 
the invention of the ophthalmoscope.' Helmholtz 
was visibly moved, and when he went home beloved 
lips said to him ' Better than a decoration r ' To 
which he replied, c Certainly ; it is a decoration on 
the part of competent judges.' 

Long afterwards, on gth August 1886, at the fifth 
centenary of the University of Heidelberg, there was 
another great meeting of ophthalmologists, and Helm- 
holtz was presented with the von Graefe medal, a 
memorial of the great ophthalmologist, awarded every 
tenth year to the man of whatever nation who has 
rendered the greatest service to the science of ophthal- 
mology. Professor von Zehender was in the chair, 
and in the presence of many distinguished visitors to 
the famous university on the banks of the Neckar, 


Donders, in a brilliant speech, made the presentation. 
After a brief survey of Helmholtz's career, he con- 
cluded thus: 'And now, twenty-eight years after 
that memorable day, highly esteemed and honoured 
von Helmholtz, I turn to you in the name 
of that society for which von Graefe then spoke, 
and so to say, in his name, in the name of our 
master and patron, offer you the first honorary medal 
instituted in his memory. May this gift hereafter, 
when following the first modest tribute which our 
society long since ventured to offer you, Science 
from its highest circles, and your Emperor, whom 
you reverence and esteem, shall have heaped upon 
you all the distinctions suitable to great endowments, 
associated with great deserts ; may this gift still 
remain to you a gratifying symbol of the privilege 
you enjoy of living in a generation that honours you 
as its benefactor. May this happy knowledge, which 
is not granted to every man of genius, illumine with 
its gentle light this evening of your life, in which 
you may see yourself always surrounded in unfading 
freshness of mind and body by the love of all that 
are dear to you.' 

Helmholtz replied, and gave an interesting sketch 
of his contributions to science in the domain of physio- 
logical optics. He referred with great modesty to 
the invention of the ophthalmoscope, and to its im- 
portant uses in the hands of ophthalmologists, in the 
following beautiful words : c Let us suppose that up 


to the time of Phidias nobody has had a chisel suffi- 
ciently hard to work on marble. Up to that time 
they would only mould clay or carve wood. But a 
clever smith discovers how a chisel can be tempered. 
Phidias rejoices over the improved tools, fashions with 
them his God-like statues and manipulates the marble 
as no one has ever done before. He is honoured and 
rewarded. But great geniuses are most modest just 
in that in which they most excel others. That very 
thing is so easy for them that they can hardly under- 
stand why others cannot do it. But there is always 
associated with high endowments a correspondingly 
great sensitiveness for the defects of one's own work. 
Thus, says Phidias to the smith, "Without your aid 
I could have done nothing of that ; the honour and 
glory belong to you." But the smith can only 
answer him, "But I could not have done it even 
with my chisels, whereas you, without my chisels, 
could at least have moulded your wonderful works 
in clay ; therefore I must decline the honour and 
glory, if I will remain an honourable man." But 
now Phidias is taken away, and there remain 
his friends and pupils Praxiteles, Paionios, and 
others. They all use the chisel of the smith. The 
world is filled with their work and their fame. They 
determine to honour the memory of the deceased with 
a garland which he shall receive who has done the 
most for the art, and in the art, of statuary. The 
beloved master has often praised the smith as the 


author of their great success, and they finally decide 
to award the garland to him. " Well," answers the 
smith, " I consent ; you are many, and among you 
are clever people. I am but a single man. You 
assert that I singly have been of service to many of 
you, and that many places teem with sculptors who 
have decked the temples with divine statues, which, 
without the tools that I have given you, would have 
been very imperfectly fashioned. I must believe you, 
as I have never chiselled marble, and I accept thank- 
fully what you award to me, but I myself would have 
given my vote to Praxiteles or Paionios." ' 




FROM 1851 to 1856, when he went to Bonn, 
Helmholtz was mainly engaged in researches 
in physiological optics. Now and again he entered 
on electrical problems, two papers appearing in 1851 
on the induction coil. In 1852 he gave an interest- 
ing resume, characterised by much critical acuteness, of 
the progress of electro-physiology, or animal electri- 
city, up to that date. It was in 1851 that he began 
the systematic examination of the eye, both as regards 
its anatomy and its physical constants, an examination 
that culminated in his great work on physiological 
optics ; and it was also in 1852 that he invented the 
ophthalmometer. In this year he also wrote an im- 
portant paper on the theory of heat as applied to 
living beings ; a paper dealing with the relation of heat 
to work appeared in 1855. Further, it was in 1852 
that problems of a psychological nature first occupied 
his attention. The publication of the results of his 
investigations into these problems first began in 1852 
with a short but fundamental paper on the nature of 


sensation, and then there followed in rapid succession 
a series of papers on the phenomena of colour. The 
first announcement of research into acoustical ques- 
tions was also made in 1852, a subject which occupied 
much of his attention till 1863, when he published 
his great work on Sensations of Tone as the Physio- 
logical Basis of Music, a work that may fitly be called 
the Principia of acoustics. It was probably in Konigs- 
berg that his genius burst forth in all its splendour, 
although it had not yet reached its zenith, and this 
period was characterised by intense mental activity, 
as indicated both by the far-reaching nature of the 
problems he attacked, and by the success with which 
he achieved at least their partial solution. 

The University of Konigsberg may well be proud 
of her famous professor. The distinguished man who 
now occupies the chair of physiology there, Professor 
Ludwig Hermann, in an address on Helmholtz, 
remarks with pardonable pride : * In a little room in 
the anatomical department, which was his workshop, 
originated the myographion, the ophthalmometer, and 
the ophthalmoscope. His models were first con- 
structed with his own hands, chiefly with wire, cork, 
and sealing-wax, and then they were completed by 
Rekoss.' In these days of palatial laboratories spring- 
ing up all over the world in connection with each 
department of science, it is well not to forget that 
some of the greatest results in science have been 
gained in humble rooms and with simple appliances. 


Neither the most splendid buildings, fitted with the 
most modern appliances, nor the endowment of 
research, however wisely conceived, will compensate 
for the absence of genius. The living spirit must be 
the propelling force, and whilst it is reasonable that 
every facility for research should be afforded, a view 
which is now recognised in every civilised country, 
and mostly by those nations that form the vanguard 
of progress, there still remains the fact that in Science 
as in Art the great investigator, like the great artist, is 
born, not made. 

Helmholtz, like all hard workers, needed periods of 
comparative rest, and he was wont usually to betake 
himself to the mountains and valleys of Switzerland. 
The year 1854 is memorable from the occurrence of 
his first visit to England, and in a letter written to his 
friend Ludwig, 1 after his return, we get a glimpse 
into his first impressions : 

' K.ONIGSBERG, 2, vi. 54. 

1 DEAR LUDWIG, England is a great land, and one 
feels there what a magnificent and splendid thing civili- 
sation is, and how the minutest conditions of life bear 
its impress. In comparison with London, Berlin and 
Vienna are mere villages. To describe London is 
impossible ; it must be seen with one's own eyes 
before one can attempt to form an estimate of it. A 

1 For this letter I am indebted to my friend Professor Hugo Kronecker, 
of Bern, whose Life of Helmholtz is eagerly expected. It is understood 
that many letters have been placed at his disposal. 


visit to London marks an epoch in one's life ; after such 
a visit, one learns to judge human actions on a scale 
hitherto unknown. I have been very unfortunate in 
meeting scientific men, missing Rankine, Brewster, 
Joule, Thomson, and Wheatstone, but with Faraday, 
Stokes, Sabine, Grove, Airy, Bence Jones, Andrews 
the chemist, Hamilton the mathematician, and many 
others of lesser importance, I have had better luck. 
These men seem to be as generous as Swiss tourists 
are odious ! 

' Bence Jones is "a man among men," as we say in 
Berlin. He invited me to his villa at Folkestone, on 
the sea coast, where I met Du Bois Reymond and his 
wife. Our friend has become quite an Englishman. 
I was received there as heartily as if I had been an old 
friend. I spent three weeks sight-seeing in London, 
and when I left it for the meeting (of the British 
Association) in Hull, I had not even seen the half of 
it. The organisation of the meeting at Hull greatly 
interested me. There was not much scope for 
physics, chemistry, and such like sciences, in which a 
man must work by himself, and the leaders of these 
sciences kept in the background. For other sciences, 
however, such as meteorology, ethnology and geology, 
where there must be co-operation among many ob- 
servers, the meetings (of sections) were of great 
importance. There were over 800 members, and, in 
addition, 250 ladies who came to listen. As a 
foreigner, I was the guest of Dr Cooper, a physician, 


who entertained me most hospitably. I then spent 
eight days in Scotland, to feast on nature. Edinburgh 
is a jewel among cities. The Scotch Highlands have 
a peculiar majesty, from their proximity to the 
Atlantic Ocean ; but they are, on the whole, barren 
and monotonous, and not to be compared with the 
Alps. I saw Fingal's Cave in beautiful weather, then 
unceasing rain compelled me to return. I travelled 
home via Hull and Hamburg, and arrived with a very 
empty purse. My health has greatly benefited by 
the trip, but my teeth troubled me on the journey, 
and made for a time my physiognomy asymmetrical.' 

In after years Helmholtz paid not a few visits to 
this country, and more especially to his friend of many 
years, Lord Kelvin. Between these distinguished men, 
the foremost in their time in physical science, there 
always existed the warmest friendship. Often differing 
on scientific questions, each had admiration and respect 
for the powers and achievements of the other. 

To return to the physiological work of Helmholtz 
during the early fifties, there can be no doubt the re- 
searches on the mechanism of accommodation and on 
sensations of colour were of the first importance. His 
singular combination of anatomical, physiological, phy- 
sical, and mathematical knowledge fitted him specially 
for this work. Up to his day no one had appeared like 
him in this respect, and it may be questioned if any- 
one now exists who can be placed on the same platform 


with Helmholtz, much as many physiologists, especially 
in Germany, now cultivate physics and mathematics. 

The ophthalmometer, an instrument of too technical 
a character to be here described, 1 enabled Helmholtz 
to determine many of the optical constants of the eye, 
more especially as to the radii of curvature of the re- 
fractive surfaces, the cornea and lens. He was also 
able to solve the interesting problem as to the focussing 
or accommodating mechanism of the eye, by which it 
adapts itself for distinct vision within a certain range. 

In the normal eye parallel rays coming from infinity 
are brought to a focus on the retina, and a distinct 
image is formed. When rays are not brought accu- 
rately to a focus on the retina, the image is indistinct, 
by the formation of circles of diffusion around its 
margin. It is evident that if an object be brought 
too close to the eye for the refractive media to focus 
it on the retina, circles of diffusion will be formed, 
with the result of causing indistinctness of vision, 
unless the eye has some power of altering its length 
or the curvature of its refractive surfaces. That 
the eye has some such power of accommodation is 
proved by the observation that if we look through the 
meshes of a net (the net say 3 feet from the eye) at 
a distant object, we cannot see both the meshes and 
the object with equal distinctness at the same time. 
At one moment the meshes will be seen distinctly 

1 Fully described in Appendix D, p. 718, of my Outlines of Physiology. 
Glasgow, 1878. 



and at the next the distant object. Again, if we 
persistently look at objects close to the eye, say 
within 6 inches, there is a sense of effort and the 
eye becomes fatigued. The range within which the 
accommodating mechanism works is, in the normal 
eye, from 65 metres (about 70 yards), the so-called 
punctum remotum^ to ith metre (20 centimetres, say 
10 inches), the punctum proximum. Beyond 65 metres 
rays emanating from an object may be practically 
regarded as parallel, and they will be focussed on the 
retina without effort ; from 65 metres to ^th metre 
the accommodating mechanism comes into play so as 
still to bring the more divergent rays to a focus on 
the retina, and thus secure distinct vision ; and 
lastly, within a distance of 4th metre (except in juvenile 
life) the accommodating mechanism ceases to act, the 
rays that enter the pupil are now too divergent to be 
focussed on the retina, and there is blurred vision. 
If we cut off the more divergent rays by looking at 
the near object (say 2 inches from the eye) through 
a hole in a card, then we can see the object dis- 
tinctly as we now use the central pencils of rays 
which may be slightly divergent or nearly parallel. 
The pupil, the diameter of which is lessened by con- 
traction of the iris, serves the same purpose. Con- 
sequently, when we look at a near object the pupil 
contracts. The question arises, how is this wonderful 
mechanism carried out ? 

If we hold a lighted candle in front, and a little to 


the side of a living eye, three reflections, or little 
specks of light, may be seen in the eye. The brightest 
one, an erect image, is on the anterior surface of the 
cornea ; the next, also erect, but much less distinct, 
is on the anterior surface of the crystalline lens ; and 
the third, extremely faint and difficult to see, is 
inverted and comes on the posterior surface of the 
lens. The one on the anterior surface of the cornea 
has no doubt been long familiar, the 'light of the eye,' 
represented by artists in a portrait by the little speck 
of yellowish white paint. The next, on the anterior 
surface of the lens, was long ago observed by Sanson, 
who looked for it in connection with the appearance of 
cataract ; while the third was first discovered by one of 
the older physiologists Purkinje, who detected many 
things, so that his name appears in every physiological 
text-book. A Dutch observer, Cramer, made the 
happy observation that if the eye suddenly transfers 
its gaze from a distant to a near object, the middle 
image moves nearer the most anterior image, and at 
the same time becomes smaller. As this image is a 
reflection from the anterior surface of the lens, and 
as an image on a more convex lens is always smaller 
than one on a less convex surface, it will be evident 
that when the eye focusses on the retina the more 
divergent rays that come from a near object, it 
changes its curvature and becomes more convex. 
Accommodation, then, consists in an increasing 
convexity of the lens, beginning when the eye looks 


at an object at a distance of 65 metres and ending 
when the near point is reached at a distance of 
^th metre. 

Before these observations were made, the most 
diverse views had been advanced by physiologists as 
to the mechanism of accommodation. Some denied 
that any change took place in the refractive media, 
and also that any change was necessary ; others, that 
a change took place in the form of the globe of the 
eye, the organ becoming compressed by the muscles 
that move it, so that it became slightly longer for 
near objects than for those at a great distance ; others, 
that the contraction of the pupil that takes place 
when we look at a near object is sufficient to explain 
the mechanism ; others, that there was a change in 
the curvature of the anterior surface of the cornea ; 
others, that the lens was displaced backwards or for- 
wards by the mucular iris ; while, finally, the true 
explanation, verified by the facts already stated, had 
many supporters from the time of Descartes down- 
wards. The first correct observation was undoubtedly 
made by Thomas Young. 1 His experiment consisted 
in looking through wire gauze at a luminous point. 
An image of diffusion is then seen, traversed by 
straight lines, which are the shadows of the wires of 
the gauze. These lines are quite straight when we 
look at a distant object, but they appear to be curved 

1 Phil. Trans. 1801, vol. i., p. 23, also vol. i. of Kong's Works, 
edited by Peacock. London, 1855. 

9 6 


at their extremities if the eye is directed to an object 
close at hand, a result that can only be explained by 
supposing that the lens becomes, in the latter case, 
more convex. This experiment, difficult of execution, 
excited the admiration of Helmholtz, who always 
regarded Young as a man before his time, and one of 
the greatest of English philosophers. Max Langen- 
beck, 1 about 1849, came near the true explanation, 
but it was reserved for Cramer to complete the dis- 
covery. He observed the image of a flame, reflected 
from the anterior surface of the lens, by means of a 
short focus telescope, and noticed the essential fact 
that the image became smaller when the eye was 
directed to a near object. 

Helmholtz, unacquainted at the time with the 
work of Langenbeck and Cramer, now took up the 
question, and, with his usual thoroughness, went to 
the bottom of it. He arrived at the same conclusions 
as Cramer, but he went much farther. Here, again, 
there was no question of priority. When Cramer's 
work was brought under his notice by the writings 
of his friend Donders, who rescued Cramer from 
oblivion, 2 Helmholtz at once recognised his merits. 
Donders, in the speech already referred to, said : 
' If it be a satisfaction to me to venture to claim 
the first for my countryman, D. A. Cramer, I must 

1 Klinhche Beitrage. Gbttingen, 1849. 

- Tijdichrift der Maatschappy -voor Geneeskunde, 1851, vol. xi., p. 15 ; 
also Nederlandsch Lancet, z i. p. 529, 1851-2. 


not omit to state that Helmholtz shortly afterwards 
arrived independently at the same result. With a 
noble modesty, for which I thank him, he declared 
himself convinced, after an examination of the papers 
sent to him, that the enigma of accommodation, upon 
which so many enquirers had exhausted their in- 
genuity, was in reality solved as to the main point, 
and very little now remained for him to do in the 
researches he contemplated.' Helmholtz, in the first 
instance, contrived a little instrument, the phakoscope, 
by which the images in the eye may be seen even 
better than in a darkened room. Then he invented 
an instrument for the purpose of measuring the size 
of any image reflected from a curved surface. This, 
one of the most ingenious devices, is known as the 
ophthalmometer. It depends essentially on the displace- 
ment to one side caused by holding a plate of thick 
glass obliquely in front of any object. The object 
may thus be displaced through a distance equal to its 
breadth, and the angular movement may be read off" 
on a graduated disc attached to the axis rotating the 
glass plate. Helmholtz used two plates, rotating in 
opposite directions, so that the object was displaced 
both to the right and left, and the image was viewed by 
a short focus telescope placed behind the plates. The 
instrument may be graduated empirically, or it may 
be used with the aid of a formula by which the size 
of the object may be readily calculated. An image 
is first obtained by throwing into the eye reflec- 
98 ^ 


tions from three little mirrors placed on a rod in the 
same plane as that of the eye under examination. These 
little specks of light are thus seen in a straight line, 
reflected on the anterior surface, say, of the cornea, 
and the distance between the two most distant specks 
is the breadth of the image ; the third little speck 
is exactly midway between the other two. The 
ophthalmometer is then, from a suitable distance, 
directed towards the eye, and the plates are rotated 
until the object divides into two, and the displace- 
ment is continued until there has been an apparent 
movement through the breadth of the object. The 
angular displacement is then noted, and, as already 
stated, by the use of a formula, the size of the re- 
flected image may be calculated in, say, millimetres, or 
fractions of a millimetre. Finally, if the size of the 
real object (the distance between the two mirrors 
farthest apart on the rod), the distance of the plate 
from the eye (the vertex of the cornea), and the size 
of the reflected image (as measured by the ophthalmo- 
meter), are given, it is easy to calculate the radius 
of curvature of the reflecting surface. Helmholtz, 
by means of this beautiful arrangement, was able to 
show ( i ) that the radius of curvature of the cornea for 
near and distant objects does not change 5(2) that the 
length of the radius of curvature of the anterior sur- 
face of the lens, when the eye looks at an object far 
away, is 10 millimetres, and is only 6 millimetres 
when the eye looks at a near object, that is to say, 


in the latter case, the anterior surface of the lens 
becomes more convex ; (3) that the posterior surface 
of the lens also becomes slightly more convex, as 
for near objects the radius of curvature becomes 
shorter (5-5 mm.) than for distant objects (6 mm.) ; 
(4) that when we look at a near object, the distance 
of the vertex of the cornea from the anterior surface 
of the lens becomes shorter (3-3 mm.) than for a 
distant object (3-7 mm.) ; and that during accommo- 
dation the lens becomes thicker, being 3-8 mm. in 
thickness for a distant object and 4*3 mm. for a near 
object, or from, approximately, a ^th to a 4th of an 
inch. This amount of change is quite sufficient to 
bring to a focus on the retina rays of light emana- 
ting from an object looked at within the limits of 

It only remained to explain how the curvature of 
the lens can thus be changed, and here Helmholtz 
brought his anatomical knowledge to bear upon the 
question. Thomas Young, and many of the older 
observers, thought, erroneously, that the lens was a 
muscular structure. 1 C. Weber, about 1850, electric- 
ally excited the eye, and observed the anterior surface 
of the lens moving towards the cornea. Cramer 
also electrically irritated the eye, and concluded that 
a change of form was produced by contractions of 
muscular structures in the eye itself, and he attributed 

1 Disytii sit tones quae ad facultatem oculum accommodandl sfectant. Mar- 
burg, 1850, p. 31. 


the movements chiefly to the iris. This muscular 
structure contains both circular and radiating fibres. 
As a matter of fact, distinct radiating fibres cannot 
be seen in microscopical preparations. Suppose both 
circular and radiating fibres contracted simultaneously, 
then, according to Cramer, the circular fibres offered 
resistance to the contraction of the radiating fibres, 
and thus the parts of the lens behind them, that is 
near the margins, were compressed, while the central 
part of the lens, meeting with no resistance behind 
the pupil, was pressed forward. Bonders next 
attached importance to the fringe of elastic tissue 
on the inner wall of the canal of Schlemm, from which 
both the fibres of the iris and of the ciliary muscle 
appear to originate. The latter muscle is a fringe 
of muscular tissue, the fibres of which radiate back- 
wards, and are attached to the ciliary processes of the 
choroid or vasculo-pigmentary coat of the eye. It 
lies near the zonule of Zinn, and was at one time 
termed corpus ciliare, the ciliary body. Briicke de- 
scribed it in the following words : ' The muscle is 
very easy to find, as it is nothing else than the light 
grey ring which one finds on the outer surface of 
the anterior part of the choroid after separation of 
the sclerotic, and which has up till now played so 
unhappy a part in anatomy under the names of 
ligamentum ciliary orbicularis ciliaris^ circulus ciliaris, 
ganglion ciliare, etc.' It may now be well named the 
tensor choroidei, or, as Donders suggests, the musculus 



Bruckianus, in honour of its discoverer. Helmholtz 
took up the matter at this point, and made the happy 
suggestion, which is now universally accepted as the 
true explanation, that in accommodation the fibres 
of the ciliary muscle contract and tend to draw the 
ciliary processes of the choroid forward. Passing in 
close proximity to these processes, and connected with 
them, is a thin transparent membrane, the hyaloid 
membrane, which lines the posterior chamber of the 
eye. Anteriorly this membrane divides into two 
layers, one passing before and the other behind the 
lens, forming what is termed its capsule. The lens 
is thus bound down, as it were, by its capsule, more 
especially by the portion of it passing over its anterior 
surface. When, then, the ciliary processes are pulled 
forward by the ciliary muscle, the tension of the layer 
of the capsule in front of the lens is diminished, and 
the anterior surface of the lens bulges forward by its 
elasticity. There are certain circular fibres of the 
ciliary muscle that also assist in this beautiful 
mechanism. When the eye is again directed to a 
distant object, the fibres of the ciliary muscle relax, 
and the lens is flattened by the pressure of the 

Finally, and to complete the demonstration, Helm- 
holtz showed, that to accomplish accommodation, no 
other change in the eye is necessary, and he described 
an imaginary or schematic eye, slightly differing from 
the eye of Listing, and for this eye he calculated the 


optical constants as they exist for near and distant 
vision in accommodation. He then found that the 
positions of these constants, such as the position of 
the anterior focus, the positions of the nodal and 
principal points, and the posterior focus, varied for 
near and far vision as they would do if the only 
changes occurring during the mechanism were in the 
curvatures of the anterior and posterior surfaces of 
the lens, as ascertained by experiment and measure- 
ment by the ophthalmometer. So the question was 
finally settled. The discovery of the part played 
by the lens in accommodation is one of the greatest 
triumphs in modern physiology. Lucid mathematical 
and experimental proofs have been given of its 
correctness, and all other theories have been entirely 




IN after life Helmholtz made important mathe- 
matical and physical contributions to the theory 
of electrical actions, and it is interesting to observe, 
while the fact is in keeping with the plan of his 
whole career, that he was led into this path from 
the side of physiology. Before he left Berlin, and 
while he was in Konigsberg, his friend Du Bois 
Reymond was carrying on those researches into 
animal electricity that have made him famous. 
Helmholtz witnessed and took part in many of his 
experiments, favoured him with criticisms, and solved 
theoretical problems that arose in the course of 
the enquiry, more especially as to the distribution 
of electricity on conductors of various forms. By 
using a delicate, high-resistance galvanometer, and 
by the use of non-polarizable electrodes, a new 
impulse was given to the experimental investigation 
of animal electricity. If from living muscle, for 
example, currents could be led off into the gal- 
vanometer, as had been done by Nobili about 1827 
and by Matteucci ten years later, it was manifestly 


of great importance that no contact or galvanic 
electricity should be generated by bringing the 
electrodes against the living tissue. The desideratum 
was what is now called a system of non-polarizable 
electrodes. Helmholtz tried unsuccessfully to make 
such electrodes of pure silver immersed in a solution 
of a salt of silver. Later it was found that pure 
zinc amalgamated on the surface, and immersed in 
a saturated solution of sulphate of zinc practically 
fulfilled the conditions, a result that could not have 
been theoretically anticipated, and was discovered by a 
lucky hit. With pads of blotting paper immersed 
in zinc troughs containing the solution of sulphate 
of zinc, and with pads of sculptor's clay moistened 
with saliva laid on the paper pads to protect the 
muscle from the irritant action of the sulphate of 
zinc, perfect non-polarizable electrodes were obtained. 
It was then demonstrated that if a living muscle, 
say the gastrocnemius of a frog, is cut in transverse 
section, and if one clay point is applied to the middle 
of the longitudinal surface and the other to the middle 
of the transverse section, a current will flow through 
the galvanometer in such a direction as to indicate 
that the surface is positive to the transverse section. 
To explain these phenomena, Du Bois Reymond 
advanced a physical theory which may thus be 
shortly described. If we take a cylinder of zinc, 
having a bit of copper soldered on each side, and 
plunge it into dilute sulphuric acid, or even water, 


there are formed an infinite number of currents, 
which travel through the water from the zinc to the 
copper, and a portion of these may be conveyed by 
conductors applied to the zinc and to the copper. 
If, then, a galvanometer be interposed in the circuit, it 
will be found that the zinc, forming the centre of the 
cylinder, is positive, and that the copper, forming the 
sides, is negative, a result comparable to that obtained 
from a muscle. Du Bois Reymond therefore sug- 
gested that each muscular fibre is composed of an 
infinite number of small electro-motive elements, 
analogous to the cylinder composed of zinc and 
copper above described. Each little element would 
have a positive equatorial zone and two negative polar 
zones, and we may conceive it to be plunged into an 
intermediate conducting material. He did not mean 
that these electromotive molecules, or ' carriers of 
electromotive force,' existed in any histological sense ; 
they were to be regarded as nothing more than 
' the foci of chemical change,' and they were analo- 
gous to the molecules entering into the conception 
of the physicist when he discusses electrolysis. 

Du Bois Reymond, in his earlier experiments, 
thought he obtained a current from an uninjured 
muscle, that is, from one whose longitudinal and 
transverse sections were natural and not artificially 
produced. Later, however, he discovered that if 
special precautions had been taken not in the slightest 
degree to injure the muscle, no current was obtained 
1 06 


in the resting state, though on the production of 
tetanus, caused by irritating the nerve supplying the 
muscle, a negative variation, or current in the opposite 
direction, was observed. If a current were obtained 
when the muscle was at rest, it was in greatly 
diminished amount, and might even be in a con- 
trary direction. This was explained by supposing 
that in the uninjured muscle, the tendonous end, 
which is the natural transverse section, contains a 
layer of electromotive molecules, with their poles 
reversed, so that their positive surface is towards the 
transverse section. This layer Du Bois Reymond 
termed the parelectrotonic layer, and when one 
removes it by making an artificial cross section, the 
full muscle current is obtained. 

The laws of the dispersion of currents in irregularly 
shaped conductors had been only partially determined 
for conductors of two dimensions by Kirchhoff, and for 
three by Smaasen, but the results were not sufficient 
for the complicated conditions of a muscle. It was 
also difficult to show, on the electromotive molecule 
theory, why weak currents could be obtained from 
a point say in the centre of the transverse section and 
any other point in the transverse section near the peri- 
phery, and also between a point in the equatorial region 
of the muscle, on its surface, and any point nearer each 
end. These results could not be explained by the 
copper-zinc model. Helmholtz stepped in here, and, 
by his analytical power, developed the theory of 


current distribution in non-prismatic conductors. 
He showed that, on the assumption of peripolar 
molecules in the muscle substance, no weak currents 
could occur on the surface or in transverse sections, 
and that the difference of potential between the 
surface and the transverse section would not increase 
with the size of the muscle. He also showed that 
the differences between the results of the actual 
experiment and what was to be expected from Du 
Bois Reymond's assumption might simply be due to 
the weakening of the electromotive forces by contact 
with air, with fluids such as are used in the experiment, 
and by dying of the muscle substance. Further, he 
argued that the electromotive forces in the muscle, and 
certainly in the model, are modified by polarization. 
Subsequent experiments by Du Bois Reymond him- 
self, and especially by Hermann, support this view. 

In the address given by Donders, when he presented 
Helmholtz with the von Graefe medal, he said that 
the latter had denied the pre-existence of electro- 
motive forces in muscle. This observation evidently 
caused some annoyance to Du Bois Reymond, as, in 
his eloge on Helmholtz, he repudiates the statement. 
No doubt, in one of his writings, Helmholtz indicated 
that in the uninjured muscle no current could be 
demonstrated between the surface and the natural 
cross section (tendon), but he explained to Du Bois 
Reymond that this was a mistake, and that the unin- 
jured natural cross section was either weakly negative 


or neutral, and sometimes even weakly positive to the 
longitudinal surface. Du Bois Reymond further 
states : c But so little did Helmholtz intend to deny 
the pre-existence of electrical forces in muscle, that, 
on the contrary, in the paper we are here considering, 
he allows my hypothesis of the peripolar electromotive 
molecules full play as the cause of the muscle current, 
and declares, in so many words, " it stands to reason 
that the electric forces of the current-surrounded 
molecules must be taken into account in any theory 
of their movement." ' Further, Helmholtz suggested 
a theory to Du Bois Reymond in which the electro- 
motive effects were harmonised with the phenomena 
of muscular contracility, but this does not appear to 
have been published. 

These views of Du Bois Reymond, which had at 
all events the qualified support of Helmholtz, found an 
opponent in Ludwig Hermann, then professor in 
Zurich, and now in the chair in Konigsberg, once 
occupied by Helmholtz. He demonstrated that in the 
absolutely uninjured frog's muscle there is no current, 
and showed conclusively, that the current of the rest- 
ing muscle, when it is cut in transverse section, as 
directed by Du Bois Reymond, causes the death of a 
thin layer of the muscle, and so produces difference of 
potential. This difference theory refers all electro- 
motive effects of muscle to two kinds of physiological 
change. The first part of the theory is, that the dying 
portion of the substance behaves itself negatively to 


the living, and the electromotive force has its seat 
in the demarcation zone between the living and the 
dying. To this he adds a rider, that not only death, 
but irritation as well, causes the affected substance to 
become negative to the unaffected portion. He 
further shows that the really important electrical 
phenomenon is the negative variation, that is the 
current flowing in the reverse direction when the 
muscle is caused to contract, now called the action 
current. Still it must be observed that Hermann's 
statement is no final explanation. It does not explain 
why the dying muscle becomes negative to the living, 
and it is possible that again we may be obliged to have 
recourse to some such hypothesis as that of Du Bois 

Helmholtz, when he was showing electrical experi- 
ments of this nature to his audience of students at 
Konigsberg, hit upon the device (not original, how- 
ever) of attaching a bit of silvered glass to the astatic 
needle of his galvanometer, and by this means he 
reflected a beam of light on a screen, thus making it 
possible to see at a distance the smallest movement of 
the needle. This method was independently employed 
for the galvanometer and electrometer by Thomson 
(now Lord Kelvin), and it has adaptations well known 
in every laboratory. It was about this time also 
that he perfected the arrangements for equalising the 
opening and closing shocks of the induction coil 
described in chapter iv., p. 36. 


His physiological work also led Helmholtz to in- 
vestigate the phenomena of induction currents, more 
especially as to their duration. He also studied the 
physiological effects, observed by Briicke, of electric 
shocks of extremely short duration in large conductors 
applied to the human body. These researches led to 
the invention of the well-known pendulum myograph. 

Du Bois Reymond mentions as an amusing example 
of Helmholtz's untiring energy that, as a recreation 
between periods of intense mental activity, he was in 
the habit of watching through a telescope the good 
people of Konigsberg as they walked along the streets 
near his laboratory. Weber had studied human loco- 
motion, describing and drawing the movements of 
the limbs. Helmholtz found that Weber had made 
several mistakes, more especially as to the way of put- 
ting down the foot, and his observations were verified 
long afterwards by instantaneous photography and by 
other methods devised by Marey, 1 Professor of Physi- 
ology at the College of France. 

1 E. J. Marey, Animal Mechanism, Book II., chap. iii. London, 1874. 




FROM 1852 to 1856, when he removed to 
Bonn, Helmholtz was much occupied with 
the phenomena of colour. Thus, in 1852, there 
appeared the paper on Sensation already alluded to ; 
two papers, the first mainly critical, and the second 
more constructive, on Sir David Brewster's Analysis 
of Sunlight, and a fundamental paper on the Theory 
of Colour ; and in 1855 we have three papers, all 
dealing with colour sensation. As often happens, 
the minds of men of science in different parts of the 
world may be occupied with the same question about 
the same period of time. The rifts in the clouds 
through which shafts of sunlight pass down to the 
earth may be observed only by the few, but here and 
there, in the crowd, the eyes of keen observers are 
attracted by their beauty. Just about this time the 
phenomena of colour were almost simultaneously 
before the minds of Sir David Brewster, James Clerk 
Maxwell, and Helmholtz. Brewster was first in the 
field, his paper appearing in The Transactions of the 
Royal Society of Edinburgh in 1822. The first pub- 


lished paper of Maxwell was a letter to Dr George 
Wilson, to be found in the Transactions of the Royal 
Society of Arts for 1855, but he had before this date 
been experimenting with his well-known colour top, 
and the results of his experiments are recorded in 
the Transactions of the Royal Society of Edinburgh, 
vol. xxi., p. 185. As already mentioned, in 1852, 
Helmholtz published his first paper. 

To appreciate the work of these distinguished 
men, and more especially the part taken by Helm- 
holtz in placing the theory of colour on a sound 
basis, let us go back for a little to fundamental 
ideas regarding light, gradually accumulated before 
they appeared on the scene. It was once held 
that a luminous body shoots out from itself minute 
particles, which, passing to the observer's eye, give 
rise upon impact to the sensation of light. This 
corpuscular theory, while it satisfactorily explained 
many of the facts, failed in an explanation of others, 
and it has now been entirely disproved. Its place is 
taken by the undulatory theory, first suggested by 
Huygens in 1690, reconciled to some extent with the 
discoveries of Newton by Euler, advocated by Hartley, 
and finally established by a study of the phenomena of 
interference by Thomas Young and by Fresnel. This 
theory gives a complete explanation of all the pheno- 
mena of light. According to this view, light, objec- 
tively considered, is simply a mode of motion of a 
substance called the luminiferous ether which pervades 


not only what is commonly regarded as space, but 
also all translucent substances. By the molecular 
movements of luminous bodies, this ether is set vibrat- 
ing in a series of waves. The ether vibrations that 
constitute these waves may be conceived to be at 
right angles to the direction of the ray of light, just 
as the surface of calm water, which has been agitated 
by a stone, rises and falls as the waves spread outwards. 
Thus a cork floating on the water, traversed by a 
wave, oscillates up and down nearly at right angles to 
the direction of the wave. These wave-like move- 
ments of the ether impinging on the retina set up in it 
changes which result, after their effect has been trans- 
mitted to the brain, in the sensation of light, but the 
sensation in no way resembles its physical cause, 
although it varies with variation of the stimulus. 1 
The intensity of the sensation varies with the ampli- 
tude of the wave. Large waves give rise to a sensa- 
tion of bright light, small waves to a sensation of dim 
light. Again, the sensation of colour depends on the 
rapidity with which the waves follow one another, or, 
in other words, on the length of the wave. This 
rapidity, though inconceivably great, may still be 
accurately determined. Ordinary sunlight, as Newton 
showed, is composed of a series of colours (using the 
word in an objective sense) blended together, but yet 
separable from one another, because each colour is due 

1 Physiology of the Senses. By M'Kendrick and Snodgrass. London, 
1893, p. n S . 


to a series of waves differing in rate of succession from 
the others. Thus the waves that give rise to a sensa- 
tion of red light follow each other at the rate of about 
435 millions of millions per second, while those of 
violet light succeed each other at about 764 millions 
of millions per second. Between these we have an 
infinite number of series of waves, each giving rise 
to a special colour sensation, and so between the red 
and the violet of the spectrum we have a gradation of 
colour roughly described as orange, green, blue and 
indigo, but each of these is itself made up of countless 
shades, which melt as gradually and imperceptibly 
into one another as the colours of a sunset sky. The 
retina is not sensitive to vibrations of the ether suc- 
ceeding each other more slowly than those of red 
light, although it may be demonstrated that these 
exist and originate electrical and thermal phenomena ; 
nor to those which come more quickly, although the 
latter have marked chemical activity, and give rise 
to fluorescence. 

Solar or white light is, then, a compound of all the 
colours in definite proportion. A body which reflects 
solar light to the eye without changing this propor- 
tion appears to be white ; but if it absorbs all the 
light, so as to reflect no light to the eye, it appears to 
be black. If a body held between the eye and the 
sun transmits light unchanged and is transparent, it 
is colourless ; but if translucent, it is white. If it 
transmits or reflects some rays and absorbs others, it 


is coloured. If, for example, it absorbs all the rays of 
the solar spectrum but those which give rise to the 
sensation of greenness, we say that the body is green 
in colour. But this greenness can only be perceived 
if the rays of light falling on the body contain rays 
which have the special vibratory rate that is required 
for this special colour. For, if we use as our light 
any other pure-coloured ray of the spectrum, say the 
red, its rays being absorbed, the body appears to us to 
be black. A white surface seen in a red light seems to 
be red, in a green light green, as it reflects all colours 
alike, absorbing none. To the normal eye the colour 
physically depends, then, on the nature of the surface 
of the body, as was first shown by Robert Boyle, 
and of the light falling upon it, and the sensation of 
colour only arises when the body reflects or transmits 
the special rays to the eye. If two rays of different 
wave-lengths affect one part of the retina at the same 
time, they are fused together, and we have the sensa- 
tion of a third colour different from its cause. Thus, 
if red be removed from the solar spectrum, all the 
others combined will give a sensation of a greenish 
yellow, although we cannot, with the unaided eye, 
analyse this into its components. Certain colour 
sensations, such as red or green, are simple in the 
sense that they cannot be originated by any combina- 
tions of other colours ; while other colours, such as 
purple, can be produced by certain definite mixtures, 
and they are therefore called compound. 


Newton laid the foundation of the theory of com- 
pound colours. He showed that two beams that differ 
optically, that is as regards the periods and amplitudes 
of their ether vibrations, may be alike chromatically, 
that is to say, they may give rise to the same kind of 
colour sensation. Thus, by mixing red and yellow, 
an orange colour may be produced like that of the 
spectrum, but differing from it in that the former may 
still be analysed by a prism into red and yellow, whereas 
the orange of the spectrum cannot be so resolved. 
By his well-known diagram of colour, Newton also 
showed that in any mixture of colours, the quantity 
and quality of each being given, it was possible to 
determine the colour of the compound. While the 
result of mixture of colours in the production of 
compounds can thus, by a geometrical method, be 
represented with approximate correctness, their true 
relations, as was shown by Clerk Maxwell, 1 can only 
be determined by direct experiment. 

With his usual experimental dexterity and philoso- 
phical acumen, Thomas Young was led to a great 
generalisation on the subject of colours, in which it is 
asserted that the three simple colour sensations are 
red, green and violet, and while these cannot be 
produced except by the impact of light of a certain 
wave-length on the retina, and are therefore simple, 
any other colour may be matched by a mixture of 

1 An interesting account of Clerk Maxwell's work on the subject is 
given by Glazebrook in his Life of Max-well. London, 1896, p. 93. 


these three primaries. The quality of the compound 
colour so produced depends on the proportion of the 
intensities of the components, and its brightness 
depends on the sum of these intensities. There is no 
proof that these effects depend entirely on changes 
occurring in the retina ; the probability is, as was 
indeed suggested by Young himself, that they are 
connected with phenomena occurring in the brain. 

Sir David Brewster r developed a new theory of 
colour sensation, in which the three primitive colours 
were red, yellow and blue, 2 and it was assumed that 
they corresponded to three kinds of objective light. 
Each of these varieties gave throughout the spectrum 
rays of all degrees of refrangibility, but the red pre- 
dominated at the lower end, blue at the upper end, 
while yellow ruled the middle. Coloured media 
absorbed in different proportions rays of the same re- 
frangibility, but of different colours. This theory was 
combated by Airy, Draper and Melloni, and it has 
now been entirely abandoned. It was founded mainly 
on the colours apparently assumed by light in passing 
through various transparent and colourless media ; 
phenomena, however, that can be explained by disper- 
sion or diffusion even in clear prisms and in the media 
of the eye. Brewster's investigations undoubtedly 
led to renewed research, and it was at this point 

1 Trans, of Royal Soc. of Edinburgh, ix., p. 433 ; xii., p. 123. Pogg. 
Annalen, xxiii., p. 435. 

1 Leonardo da Vinci, Trattato della fittura, Paris, 1651, named four 
simple colours, yellow, green, blue and red. 



Helmholtz took up the subject. We have it on his 
own authority, that his attention was directed to it by 
a consideration of Miiller's doctrine of the specific 
energy of nerves, mentioned at p. 13. In his speech 
on receiving the Graefe medal, he said, c Not being 
inclined to describe in my lectures things I had not 
myself seen, I made experiments in which I blended 
the colours of the spectrum in pairs. To my aston- 
ishment, I found that yellow and blue gave not green, 
as was then supposed, but white. Yellow and blue 
pigments, when mixed, no doubt gave green, and 
until then the mixing of pigments was supposed to 
produce the same effect as the mixing of the colours 
of the spectrum. This observation not only at once 
produced an important change in all the ordinarily ac- 
cepted notions of colour mixture, but it also had an even 
more important effect on my views. Two master minds 
of the first rank, Goethe and David Brewster, were of 
opinion that yellow and blue could be directly seen in 
green. Their observations were made with pigments, 
and they thought they could divide their perception 
of the resulting colour into two parts, yellow and 
blue, while in reality, as I was able to show, neither 
were present. I was thus drawn over to the em- 
pirical theory of perception, and it indicates even now 
the contrast between my position in the theory of 
colour perception and that of Hering and his followers, 
who hold firmly to the opinion, that one can decom- 
pose the perception into its component parts.' 


The true explanation of why yellow and blue 
pigments yield green may thus be shortly stated, and 
almost in the words of Helmholtz : r When light 
falls on a powder composed of transparent particles, 
only a small portion is reflected from the surface ; the 
rest penetrates the particles, and is only returned by 
the surfaces of separation of particles situated more 
deeply. Thus a single plate of clear glass reflects 
-Jgth of the light which strikes its surface, two plates 
will reflect y^th, and many plates will reflect nearly 
the whole of it. If the glass reflects only ^ T th of 
the incident light, the rest must be reflected by the 
deeper layer. In the same way the surface of coloured 
powders furnishes only a small part of the light which 
emerges from them ; the deeper parts give back a 
greater proportion. Light reflected from the surface 
is always white ; that alone which is returned by the 
deeper layers is coloured by absorption, and the tint 
will be deeper as the light penetrates more deeply. 
Consequently coloured powders are more deeply 
coloured if the grains are of considerable size than if 
they are very minute. Reflection depends on the 
number of surfaces, and not on the thickness of the 
particles. Consequently, if the particles are large, the 
light must go through a greater thickness to reach the 
same number of reflecting surfaces than if the particles 
are small, and thus, if the particles in a thick powder 
are large, the rays absorbable by the substance will be 

1 Oftiijue Pfiysiologiyue. Paris, 1867, p. 363. 
1 2O 


taken up to a greater extent, and the coloured light 
coming back from the powder will be deeper and 
more saturated than if the particles were small. Sup- 
pose, now, that yellow chrome is mixed with indigo 
blue. The light reflected from the particles of chrome 
will be orange, yellow and green, the blue and violet 
being absorbed, and that from the indigo blue will be 
green, blue and violet, the orange and yellow being 
absorbed. If, now, the light that has passed through 
a particle of chrome traverses a particle of indigo blue, 
all the colours will be absorbed except the green. 
Consequently the green alone will reach the eye. 

On the other hand, if the pure spectral colours, 
yellow and blue, pass into the eye so as to affect the 
same spot on the retina, the result is a sensation of 
white, because, in this case, both the yellow and the 
blue wave-lengths fall on the terminal organ. This 
ingenious explanation has many important applica- 
tions, not only as regards the colours reflected from 
mixtures of powders, but also the mode of action of 
all coloured surfaces both in the inorganic world and 
on the surfaces of plants and animals. It shows how 
the texture of the surface modifies the result. 

Helmholtz then devised an ingenious method by 
which two spectra could be simultaneously examined, 
through a slit shaped like the letter V, in such a way 
that a portion of one spectrum was superposed on the 
other. In this way all possible mixtures of two 
simple colours could be made with the intensities of 


the colours in the two spectra, and the mixed rays, 
passing through a lens, were directed on the same 
spot of the observer's retina. This method differs 
from that of using a rotating disc, sectors of which 
could be coloured at pleasure, a method used by 
Thomas Young, but worked out with great exacti- 
tude by Clerk Maxwell, in the form of his well-known 
colour top. The arrangement of the rotating disc is 
such that a little area of retina is struck in rapid 
succession with reflected rays of different wave- 
lengths, say now the long waves of red, then the 
short of violet, with the result that the sensation is 
that of purple. 

By mixing the pure colours of the spectrum, Helm- 
holtz showed that red and violet gave purple ; red 
and blue, rose ; red and green, dull yellow ; red and 
yellow, orange ; yellow and violet, rose ; yellow and 
and blue, white ; yellow and green, yellow-green ; 
green and violet, pale blue ; green and blue, blue- 
green ; and blue and violet, indigo ; but he was un- 
able by any combination to produce red, green and 
violet. Further, he formulated several important 
principles with regard to sensations of colour. Thus 
the quality of every luminous sensation depends on 
three variables luminous intensity, tone, and degree 
of saturation. A sensation of colour produced by a 
certain quantity, *, of coloured rays mixed in any way 
whatever may be always reproduced by a certain 
amount, a, of white light with a certain quantity, b y 


of a saturated spectral colour (or purple) of a deter- 
minate tone. From the physical point of view, mixed 
light is compounded of various waves of different wave- 
lengths ; but the sensation caused by the mixture falling 
on the retina may be always considered as a function of 
three variable quantities (i) the quantity of saturated 
coloured light ; (2) the quantity of white light which 
may be added to produce the same sensation of 
colour ; and (3) the length of the wave of coloured 
light. He also investigated mathematically the con- 
struction of a geometrical table of colours. Finally, 
he revived and extended the hypothesis of Thomas 
Young, 1 which attempted to explain and account for 
the phenomena of colour. 

How conies it that we perceive differences in 
colour ? We may look for the cause in various 
directions. We might suppose a molecular vibration 
to be set up in the nerve-endings synchronous with 
the undulations of the luminiferous ether, without 
any change in the chemical constitution of the sensory 
surface ; and we might suppose that where various 
series of waves corresponding to different colours 
act together, these are fused together, or interfere 
with each other in such a way as to give a vibration 
of modified form or rate corresponding somehow to 
the sensation arising in consciousness. Or, again, 
we might suppose that the effect of different-coloured 
rays is to promote or retard chemical changes in the 

1 Lectures on Natural Philosophy, 1807. 
I2 3 


sensory surface, which again so affect the sensory 
nerves as to give rise to differing states in the nerves 
and nerve centres with differing concomitant sensa- 
tions. The first line of thought is at the basis of 
the hypothesis of Thomas Young. He supposed that 
there are three fundamental colour sensations red, 
green and violet by the combination of which all 
other colours may be formed, and that there are in 
the retina three kinds of nerve elements, each of 
which is specially responsive tb the stimulus of colour 
of one wave-length, and much less so to the others. 
If a pure red colour alone act on the retina, only the 
corresponding nerve element for red sensation would 
be excited, and so with green and violet. But suppose 
the colour to be mixed, then the nerve elements will 
be set in action in proportion to the amount of con- 
stituent excitant rays in the colour. Thus, if all the 
nerve elements be set in action, we shall have white 
light ; if that corresponding to the red and green, the 
resultant sensation will be orange or yellow ; if mainly 
the green and violet, the sensation will be blue or 
indigo, and the like. Helmholtz succinctly puts it as 
follows : 

(i.) Red excites strongly the fibres sensitive to 
red, and feebly the other two sensation, 

(2.) Yellow excites moderately the fibres sensitive 
to red and green, feebly the violet sensa- 
tion, yellow. 



(3.) Green excites strongly the green, feebly the 

other two sensation, green. 

(4.) Blue excites moderately the fibres sensitive to 
green and violet, and feebly the red sen- 
sation, blue. 

(5.) Violet excites strongly the fibres sensitive to 
violet, and feebly the other two sensation, 

(6.) When the excitation is nearly equal for the 
three kinds of fibres, then the sensation is 

Another mode of expressing the theory is to say 
that each primary sensation of red, green and violet 
is excited in some degree by almost every ray of the 
spectrum, but the maxima of excitation occur at 
different places, while the strength of stimulation in 
each case diminishes in both directions from the 
maximum point. Thus when the three sensations 
are equally excited, white light is the result ; green 
is caused by a very weak violet stimulation, a stronger 
red, and a still stronger green stimulation. At each 
end of the spectrum we have only the simple sensa- 
tions of red and violet, and all the intermediate colour 
sensations are compounds of varying proportions of 
the three primaries. 

According to this theory, red blindness is attribut- 
able to the absence of the red sensation, and green 
blindness to the absence of the green sensation. 
When the green and violet sensations are equal in 


amount, a red-blind person sees what is to him white, 
and when the red and violet are equal, a green-blind 
person will have a sensation of what in turn is to him 
white, although, to the normal eye, these parts are 
bluish-green in the one case and green in the other, 
as the green sensation is in each added to the sensa- 
tions of red and blue. 

The subject is fully discussed in Helmholtz's great 
work, Handbuch der physlologischen Optik, the first part 
of which appeared in 1856 and the last in 1867. The 
first part of a new edition appeared in 1885, and the 
last in the year of the death of Helmholtz, 1894. In 
the new edition he returns to the subject of colour 
vision, and materially modifies the views in his earlier 
writings as to what is now universally known as the 
Young- Helmholtz theory of colour sensation. It is 
fitting that the two great names should be linked 
together. Helmholtz finally held that luminosity or 
brightness plays a more important part in our per- 
ceptions of colour than has been supposed. He also, 
by analysing the colours of the spectrum with great 
care, aided by his pupils, and more especially by 
Arthur Konig, was able from these data to determine 
three fundamental colour sensations, the first red (a\ 
which is a highly-saturated carmine-red ; the second 
green (), like the green of vegetation ; and the third 
blue (c\ like ultra-marine. Each spectral colour he 
supposed to be made up of certain proportions of these 
fundamental colours, or of a combination of two of 


them added to a certain amount of white. Thus 
100 parts of green are composed of 15 of #, 51 of />, 
and 34 of c ; or, to take other examples, spectral red 
contains, in 100 parts, 42 of #, i of , and 57 of white ; 
yellow ii of a, 14 of , and 75 of white ; and blue 
2 of a y ii of c y and 87 of white. The white gives 
the element of brightness. According to this view, 
it is not necessary to suppose that in the red- 
blind the red-perceiving elements are awanting, or 
that in the green-blind the green-perceiving elements 
are absent, but that these elements may be stimulated 
with intensities different from those affecting the 
normal eye. 1 

It is foreign to the purpose of this book to criticise 
the theory, or to contrast it with the rival theory of 
Hering, which assumes molecular processes in the 
retina of a katabolic (pulling down or disintegrative) 
and an anabolic (building up or reconstructive) kind. 
Suffice it to say, that while there are a few special 
cases not yet completely explained by the Young- 
Helmholtz theory, on the whole it accounts for 
the general facts in a satisfactory and convincing 

The investigation is eminently characteristic of 
Helmholtz. He examined the facts with the min- 
utest care, and with the aid of arrangements and 
apparatus of the most ingenious and perfect kind, and 
then he endeavoured to refer all the facts to a general 

1 M'Kendrick and Snodgrass, op. cit., p. 169. 


principle. As remarked by Sir John Herschel, 1 4 we 
must never forget that it is principles, not phenomena 
laws, not insulated independent facts which are the 
objects of inquiry to the natural philosopher. As 
truth is simple, and consistent with itself, a principle 
may be as completely and as plainly elucidated by the 
most familiar and simple fact, as by the most imposing 
and uncommon phenomenon. The colours which 
glitter on a soap-bubble are the immediate conse- 
quences of a principle the most important from the 
variety of phenomena it explains, and the most 
beautiful, from its simplicity and compenduous neat- 
ness, in the whole science of optics.' 

1 Discourse on the Study of Natural Philosophy. London, 1830, p. 13. 





HELMHOLTZ was appointed to be Professor 
of Physiology at Bonn in 1856, when he was 
thirty-five years of age, and near the zenith of his 
powers. Here he remained till 1859, when he was 
invited to the chair in Heidelberg, a position he filled 
till 1871. The three years at Bonn were charac- 
terised by the same intellectual activity. Having in 
Konigsberg laid the foundation of his great work on 
physiological optics, he next proceeded to the ex- 
amination of the sense of hearing, and here he 
conquered a new world, and made it peculiarly 
his own. Again, the guiding principle was Johannes 
Miiller's doctrine of specific energy, and again he 
proceeded step by step to survey the whole region 
of inquiry on this occasion it was acoustics from 
the point of view of the physiologist, but fully 
equipped, not only with anatomical knowledge, but 
with all the methods and modes of reasoning of the 
mathematician and physicist. 


There can be no doubt that one of the secrets of 
the marvellous activity in research of Helmholtz was, 
that there was the most intimate connection between 
his function of a professor, whose duty it was to 
teach, and that of an original investigator. Teaching 
and investigation went hand in hand. He investi- 
gated because he wished to speak of matters at first 
hand, and thus he did not merely recapitulate the 
views of others. Again and again he took up a 
problem, so that he might master it himself, and be 
enabled to make it clear to his pupils. Thus there 
was not only freshness in his teaching, as he was 
continually breaking new ground, but he was year 
by year adding to scientific knowledge. It is, of 
course, in the highest degree unlikely that the im- 
petuous and masterful intellect of Helmholtz would 
have acted otherwise under almost any circumstances ; 
but, at the same time, the circumstances in which 
he was placed favoured its development. He was 
obliged, year after year, to take a general survey of 
his science ; he was always associated with the young, 
and there is nothing more inspiring for a teacher 
than to have to satisfy young and ardent minds. 
Even if these are only the minority of a class, their 
presence is a subtle inspiration, stimulating to new 
effort. The example of Helmholtz, therefore, is a 
strong argument in favour of combining teaching 
with working ; and the results, not only in his case, 
but in many others, show that, in the advancement 


of science, it may not be the wisest course to endow 
research alone and to relegate the researcher to a 
kind of monastic solitude. It will, on the whole, be 
better for him and better for science to prosecute 
research, because he must communicate to others 
the fruits of his own labours. 

The first paper on Physiological Acoustics ap- 
peared in 1854, and consisted mainly of a review of 
the work done by others up to 1849. The ground 
having in this way been cleared, three papers appeared 
on Combination Tones in 1856, one upon Vowel Tones 
in 1857, a lecture on the Physical Basis of Harmony 
and Dissonance in 1858, another on Vowel Tones, 
and two on the Theory of Open Organ Pipes in 
1859, a paper on Musical Temperature, another on 
the Motions of the Strings of a Violin, and a lecture 
on Timbre (Klangfarbe) in 1860, a paper on Reed 
or Tongued Organ Pipes in 1861, a short paper in 
1862 on the Arabic and Persian Scales, and at last, 
in 1863, there appeared the great work, Die Lehre 
von den Tonempfindungen ah physiologische Grundlage fur 
die Theorie der Musik, or Sensations of Tone as the 
Physiological Basis of Music. A well-known mono- 
graph on the mechanics of the bones of the middle 
ear and of the drumhead (membrana tympani\ involv- 
ing an elaborate anatomical investigation of these 
organs, did not appear till 1869. 

It is difficult to give the reader an adequate notion 
either of the work on physiological optics or of that on 


physiological acoustics. They must be read, referred 
to, consulted over and over again, before one can 
appreciate the wealth of material to be found in 
these volumes. They are not merely historical 
accounts of all that has been done up to the date 
of their appearance in that particular department 
of science, but, at the same time, the bibliography 
is of the most complete description, showing the 
unwearied literary activity of the author. A notice 
is given, often critical, of the works of writers from 
the earliest down to the most recent times. In 
these notices there is a generous estimate of the 
labours of those who have gone before. There is 
an absence of polemical writing ; if the author does 
not agree with the results obtained in a particular 
research, this is frankly stated, and the experimental 
error, or the illogical result, is pointed out and calmly 
brushed aside. But great as are the merits of these 
books, even from this point of view, their charm is 
their freshness. The reader feels that the author has 
gone over every bit of the ground himself, and there 
is scarcely a page that is not enlivened by the results 
of personal research. Everywhere one feels the grasp 
of a master, whether in the exposition of the subject 
in hand or in its mathematical treatment ; and it is 
characteristic of Helmholtz that, with a kind of 
literary modesty, a profound mathematical discussion 
of a difficult question is often relegated to an appendix 
at the end of the chapter, whilst it really may con- 


tain not only the gist of the matter, but be full of 
suggestions for coming observers. 

We shall now endeavour to give a short account 
of the contributions of Helmholtz to the theory of 
hearing, and in doing so it will be more convenient 
and intelligible if we make the attempt, not in the 
chronological order of Helmholtz's papers, but in 
connection with the physiological mechanism of the 
ear itself. Sound waves are collected by the external 
ear and transmitted by the external canal or meatus 
to the drumhead. The drumhead is subjected to 
periodic pressures corresponding to the individual 
waves of sound, and thus it moves inwards with each 
pressure and outwards by its elasticity. These move- 
ments of the drumhead are transmitted across the 
middle ear or tympanum to the internal ear by a chain 
of bones, the malleus, incus and stapes. Lastly, the 
internal ear consists of a very complicated arrange- 
ment of sacs, in which lie the nerve endings immersed 
in fluid, and the nerve endings receive, in their turn, 
the pressures communicated by the chain of bones, 
ending in the base of the stapes, which fits into 
the oval window. How these nerve endings are so 
affected by these pressures as to stimulate the fibres 
of the auditory nerve is the ultimate problem of 
hearing. How do we become conscious of pitch, 
of loudness or intensity, and especially of the timbre, 
quality or klangfarbe of a tone, so that we at once 
recognise the instrument producing it, whether it be 


a trumpet, a violin or a human voice ? It will be 
evident, also, that an answer to these questions con- 
stitutes what Helmholtz calls the physiological basis 
of sensations of tone. The answer, however, cannot 
explain the aesthetic relations of music ; it cannot 
explain why, of all the arts, this is the one which, while 
it is the most intangible, yet stirs the very depths of 
our being, and gives expression to feelings, longings, 
aspirations, contemplations, that can never find full 
recognition in the most splendid efforts of the painter 
or the sculptor. The work of Helmholtz, in the 
first place, laid the physiological foundation, and after- 
wards he did little more than indicate the path along 
which we must travel from the foundation into the 
region of aesthetics. Himself a musician, not only 
in the sense of enjoying music, but also because 
he had studied theory as a musician is obliged to 
do, and because he was thoroughly acquainted with 
musical literature and especially with that of his 
great countrymen Beethoven, Mendelssohn, Wagner, 
and the brilliant galaxy of lesser German composers 
he was eminently qualified for the task. Indeed, it 
seemed as if Nature had raised in Helmholtz a man 
of such a rare combination of endowments, that she 
could safely whisper to him some of her secrets in 
this borderland of physics, physiological action and 
aesthetics, feeling assured that he would be a just and 
faithful interpreter. 

Helmholtz was the first to examine the mechanism 


of the drumhead in a satisfactory manner. Had the 
drumhead been a uniformly flat-stretched membrane, 
the amplitude of its movements, in response to the 
varying pressures of sound waves, would be greatest 
in the centre, while it would diminish as the periphery 
of the membrane was approached. Helmholtz showed 
that it is not flat, but composed of numerous fibres so 
arranged as to present the convexity of a curve out- 
wards, that is, meeting the sound waves falling upon 
them, while the membrane, as a whole, bulges in- 
wards. In this way a very small change in the 
pressure of the air causes a considerable increase in 
the tension of the fibres, and as the force exerted 
upon the handle of the malleus (the bone attached 
to the membrane) increases, the amplitude of the 
movement of that bone diminishes. Thus the special 
form of the drumhead secures a maximum of efficiency 
for tones of the feeblest intensity. 

He then proceeds to examine the mechanism of the 
chain of bones, showing that they constitute a lever 
in which the force is applied at the handle of the 
malleus where it is attached to the membrane, the 
fulcrum where the short process of the incus abuts 
against the wall of the tympanum, and the work is 
done at the base of the stapes, where it pushes into 
the oval window, on the other side of which we 
have the labyrinth. The lever is such as to diminish 
the amplitude of the movements at the base of the 
stapes, while the work is done over a smaller area 


than that of the drumhead, and thus effective, but 
very minute, pushes to and fro are communicated to 
the delicate structures in the inner ear. Helmholtz 
also investigated the little saddle-shaped joint between 
the incus and the head of the malleus, showing 
that when the drumhead was pushed in very strongly 
there was a curious rotation of the surfaces of the 
bones so that they interlocked, and thus further 
pressure could not be communicated to the stapes ; 
while, on the other hand, if the drumhead was 
distended outwards, as by inflating the tympanum 
through the Eustachian tube, there was no danger of 
pulling the base of the stapes out of its place, because 
the little joint opened up, the head of the malleus 
swinging free from the depression in the incus. 
Thus the danger of injuring the inner ear by violent 
movements of the drumhead, either outward or 
inward, is reduced to a minimum by these exquisite 
arrangements. In this investigation Helmholtz proves 
to the hilt his claim to be a competent anatomist. 

It was, however, in the region of the internal ear 
that Helmholtz won for physiological science the 
greatest triumphs. Up to the date of his investigations 
this was known almost solely to the anatomists, who 
laboriously described its various parts and covered it 
over with a barbarous terminology, which is still the 
terror of students. The physiologists had little to 
say as to its probable functions, and the mathe- 
maticians and physicists and writers on acoustics 


generally, regarded it as a wilderness of sacs and 
tubes involving problems almost incapable of solution. 1 
Musicians, on the other hand, did not expect much 
help from physical and physiological science. Imbued 
with a love of their art, they were mainly occupied 
with the consideration of its aesthetic relations, they 
were unacquainted with the methods of scientific 
analysis, and they rather dreaded investigations into 
the minute structure of the parts and also the tor- 
turing expedient of physical experiment. Why an 
octave or a fifth should be more satisfying to the 
ear than a minor third ; why certain chords had a 
character of their own ; what was the physiological 
basis of discords ; what was the true nature of beats ; 
what was the physiological significance of the pro- 
gression of the notes in a melody ; what were the 
physiological laws, if any, that regulated the develop- 
ment of musical capacity in the human race; all 
these were questions the musicians cared little about, 
and if they did allow them to occupy their attention 
they were dismissed as insoluble. Men took refuge 
in the notion that music was music because it was 
adapted to our spiritual nature, and they thought 
there was little use in endeavouring to examine the 
physical and physiological materials of which musical 
tones were composed. Helmholtz changed all this 
by attempting to give an intelligible account of the 
mechanism of the internal ear. 

1 Sir G. B. Airy on Sound. London, 1871. 


This organ, as already said, consists of a complicated 
series of sacs and tubes filled with fluid. In certain 
situations the walls of the sac contain highly-differen- 
tiated epithelial structures, which are intimately 
related to the terminal filaments of the auditory 
nerve. 1 The problem is to explain how the pres- 
sures transmitted by the foot of the stapes affect 
these terminal structures in such a way as to excite 
sensations corresponding to the pitch, intensity and 
quality of tones. 

Two small sacs, the utricle and saccule, are the first 
structures that receive the impulses of the base of the 
stapes. The utricle communicates with the semi- 
circular canals, and the saccule with the long spiral 
duct of the cochlea. The oval window, into which 
the base of the stapes fits, is covered by a membrane. 
Suppose the base of the stapes to be pushed in by the 
pressure of a wave of sound, then, since the delicate sacs 
and canals are all inclosed in cavities in the bone, having 
rigid walls, it is clear that, as the fluid is practically 
incompressible by the force applied, no movements 
could be communicated to any of the delicate nerve- 
endings. But one part of the osseous wall, next the 
tympanum or middle ear, has a round opening, also 
covered by a membrane. Thus, when the base of 
the stapes is pushed inwards, the membrane cover- 

1 In some parts of this chapter I make free use of an article on 
Hearing in Schafer's advanced Text-Book of Physiology, vol. ii., written by 
my pupil, Dr Albert A. Gray, and myself. 



ing the round window passes outwards, and thus a 
to-and-fro pressure is communicated to the fluid 
in the sacs and tubes with each pressure of a wave 
of sound. 

Helmholtz emphasizes strongly a remark first made 
by Riemann, that the dimensions of the internal ear are 
so small as to form only a small part of the wave- 
lengths, even of tones of high pitch. The whole of 
the membraneous labyrinth may be regarded as part 
of any wave acting on the ear, and the wave is not 
arrested by the labyrinth as waves of light are arrested 
by the retina, but they sweep onwards through the 
bones of the head. The fact of the labyrinth being 
so small, relatively to the size of the wave, makes no 
difference in the result ; so that the labyrinth is acted 
on in the same way, whether the ear receives a wave 
of thirty feet in length, such as is produced by the 
longest pipe in a modern organ, or a wave of two- 
thirds of an inch, produced by the highest note of a 
piccolo flute. The nerve-endings are very much 
smaller, but they also act as minute portions of any 
wave, and any reasoning as to the effect of such 
waves is quite irrespective of the small dimensions of 
the receiving organs in the internal ear. This point 
is of great importance in the consideration of the 
theory of hearing advanced by Helmholtz. 

It is clear, then, that the number of movements 
communicated to the structures in the internal ear 
in, say a second of time, depends on the pitch of the 


note, as it can be shown experimentally that as a 
note rises in pitch the number of pressures also in- 
creases. Helmholtz, for this and other purposes, 
improved the syren of Cagniard-de-Ia-Tour, and 
invented the well-known polyphonic syren now 
found in every physical and physiological laboratory. 
Another way of looking at this question of pitch is 
to say that it depends on the duration of the indi- 
vidual pressures. For example, the variation of pres- 
sure involved in a tone of 256 vibrations per second 
will last the -j^-th of a second, while that of its 
octave will last only the ^-j^th of a second. It 
is not necessary, therefore, to have a large number 
of pressures per second to arouse a sensation of a 
tone of a certain pitch ; a small number, possibly 
only a few, if they come at a given rate, will be 
quite sufficient. If now we suppose that there are 
nerve-endings, say in the cochlea, so constructed as 
to have each its own period of vibration, when 
pressures come in at a certain rate, the structures 
adapted to that rate will be thrown into action, 
and we can conceive movements to be excited. 
These movements will in some way stimulate the 
nerve-ending, and a nervous impulse will be trans- 
mitted to the brain, in which will arise, by some 
molecular process, utterly unknown, the sensation of 
a tone of that pitch. Again, on such a supposition, 
it is easy to explain intensity or loudness. This will 
evidently depend on the amplitude of movement of 


the base of the stapes, on the amplitude of the ex- 
cursions of the vibratile bodies in the cochlea, and 
on the degree of stimulus given to the nerve. 

The base of the stapes is chiefly opposite the 
utricle, although it partly abuts against the saccule. 
On the wall of the utricle, immediately in front, 
there are no nerve-endings or modified epithelium, 
but on the back wall we find a ridge called the crista 
acoustica, on which are long cells having bristle-like 
points which are directed towards the base of the 
stapes. In front of these bristle cells lies a mass of 
otoliths, or ear stones, consisting of carbonate of lime. 
The pressures must be communicated, in the first 
instance, to the otoliths, and by them to the bristle 
cells. As the bristle cells are fixed, while the otoliths 
are capable of moving backwards and forwards in a 
fluid, it is clear that one impulse from the base of the 
stapes may cause the otoliths to oscillate, and, by thus 
making a series of impacts on the points of the bristle 
cells produce in them a more or less prolonged ex- 
citation. This was the opinion of Johannes Miiller. 
Helmholtz, on the contrary, considered the matter 
from the physical point of view, and his opinion was 
that the thin membrane, bearing the bristle cells, 
will readily move to the impacts of the stapes, and 
the heavy otolithic mass, by virtue of its inertia, will 
move more slowly at first, but it will continue to 
oscillate, and thus keep up stimulation. The long 
and extremely light bristles also appeared to him to 


be well adapted for sympathetic resonance, but, as 
they were of small mass, they could not long continue 
their motion. Again, according to him, the am- 
pullae at the ends of the semi-circular canals, in which 
there are also nerve-endings similar to those in the 
crista, being wide cavities with narrow exits, are 
suitable for producing a central current, which partly 
passes into eddies, and these would deflect the bristles, 
causing an oscillation. A movement of the whole 
mass of the bristle, floating in the fluid, would not 
serve the same purpose, but discontinuous streams of 
different strengths and in different directions would 
do so effectively. Thus Helmholtz contributed to 
our knowledge of what may take place in the saccule 
and utricle and ampullae. Researches made since his 
time have suggested that these parts may not have to 
do, strictly speaking, with hearing, but with the re- 
ception of those greater variations of pressure on 
which the sense of equilibrium depends. They may 
have to do with the appreciation of mass movement, 
and only indirectly with those more delicate variations 
of pressure on which true hearing depends. 

Hitherto we have considered only the reception of 
simple harmonic (sometimes termed simple pendular) 
vibrations which are known to be physically re- 
lated to pure tones. The sensation of a pure tone, 
such as can be excited by carefully bowing a 
tuning fork, mounted on a resonance box, or by 
an open organ pipe caused to sound gently by a 


steady stream of air at low pressure, is analogous to 
that of a pure colour, such as the red, green, or violet 
of the spectrum. Such tones, however, are seldom 
heard, the majority of tones being compound and 
analogous to mixtures of simple colours, such as red 
and violet producing purple, and so on. This fact 
was long known to writers on acoustics, but it was 
Helmholtz who first made an exhaustive examination 
of such compound tones, and pointed out their im- 
portance in connection with the question of quality, 
timbre, or klangfarbe (clang tint), as he termed the 
nature of the sensation by which we distinguish one 
tone from another, although of the same pitch and 
of the same intensity. 

If we help the mind by representing to ourselves 
the varying forms of waves on the surface of water, 
some with long smooth backs, others with narrow 
crests and longer troughs, some with the slope in 
the ascent sudden and with others more gradual, we 
see that there may be an almost infinite variety of 
wave-forms. (By the term 'wave-forms' we mean 
only the manner in which the changes of pressure are 
represented diagrammatically.) So it is with sound. 
Instead of a simple pendular vibration we may have 
vibrations or pressures of complicated form, which may 
cause the drumhead to move outwards and inwards 
through a complicated path of excursion. These 
movements correspond to the action of a compound 
wave. Thus pressures of a similar character pass into 


the cochlea and sweep over the nerve-endings. The 
question is, how does the cochlea behave in such cir- 
cumstances, and will its action explain quality of tone ? 
Helmholtz attacked the problem both by analysis 
and by synthesis. In the first place, he was familiar 
with Ohm's x application in 1843 of Fourier's principles 
to the decomposition of a sound wave of any type 
into a number of simple harmonic vibrations, each 
simple harmonic vibration corresponding to a simple 
tone such as a tuning fork approximately gives. 
Fourier's 2 theorem states that any given regular 
periodic form of vibration can always be produced 
by the addition of simple vibrations having vibra- 
tional numbers which are once, twice, three times, 
etc., as great as the vibrational number of the given 
motion ; and further, if we know the amplitudes 
of the simple vibrations and the differences of phase, 
then any regular periodic motion can be shown to 
be the sum of a certain number of harmonic vibra- 
tions ; in other words, the compound wave may be 
analysed into a set of constituents of definite periods. 
Applying this to the motion of the air close to the 
ear, we find that any such motion, corresponding to 
a musical tone, may be always, but for each case 
only in a single way, shown to be the sum of simple 
harmonic motions, corresponding to the partial tones 
of this compound musical tone. 

1 Poggendorff's Annalen der Physik, t. lix., p. 513 j t. Izii., p. i. 

2 Theorie Analytlipie de la Chaleur. Paris, 1821 . 

I 44 



T T ELMHOLTZ showed next how a compound 
-- -- wave of sound might be analysed by the 
application of the principle of resonance. The air in 
any cavity or vessel, such as a bottle with a narrow 
neck, or the familiar shell held to the ear, which, 
in the days of childhood, we thought gave us the 
sound of the sea, is thrown into sympathetic vibration 
by the vibrations of any sounding body in its vicinity, if 
the vibration periods of the body and of the cavity are 
approximately the same. In the first instance Helm- 
holtz used, as had previously been done by Ohm, two 
bottles, with fairly wide mouths ; and then the size of 
the cavity could be altered by filling the bottle more 
or less full of water. Streams of air were directed 
across the mouths through flattened gutta-percha 
tubes. The bottles were tuned to b and b\ an 
interval of an octave. The sound of the first bottle 
was like the vowel U, but when the sound of the 


second was added to it the resultant sound was 
more like O. Helmholtz was able to distinguish the 
sounds in the mixture. This experiment suggested the 
use of resonators. These were, in the first instance, 
cones and cylinders made of pasteboard, and finally 
the resonators, in the hands of Rudolf Konig, a native 
of Konigsberg, now established in Paris, took the form 
of hollow brass globes, each with a narrow, nipple- 
like end, which was introduced into the ear, while the 
other was directed to the source of sound. By the 
use of a number of such resonators, each tuned to 
a particular tone, it is possible to analyse a compound 
wave of sound into its constituents. However com- 
plicated the wave may be, the ear will pick up the 
tone of the resonator, and this tone will sound loudly 
in the ear. This invention was of the greatest 
importance in practical acoustics, as it enabled the 
observer to sift a mass of sound, and it did for the ear 
what the prism of Newton did for the eye. Helm- 
holtz also worked out the mathematical theory of 
resonance in great detail. 1 Many years ago the 
writer, with a feeling of veneration, had the satis- 
faction of seeing the original resonators of Helm- 
holtz in the physiological laboratory of Heidelberg. 

Helmholtz then laid stress on the fact, that the 
ear is capable of analysing a compound tone, even 
without the aid of resonators. Musicians and 

1 For an exposition, see Lord Rayleigh on Sound, vol. ii , p 171 
London, 1894. 



physicists have long known that if a violin string is 
plucked, and attention is fixed on the sensation of 
tone, we not only hear that of the musical tone 
whose pitch is determined by the period of the large 
vibrations of the string, but in addition to this, the 
ear becomes aware of a whole series of higher musical 
tones, called the harmonic upper partial tones. The 
first one, termed the fundamental or prime partial 
tone, or the prime, is the lowest, and generally the 
loudest, of all, and it is the tone by whose pitch we 
judge of the pitch of the whole compound musical 
tone. The partials are so arranged that the first 
partial, or second harmonic constituent, is the octave 
of the prime, with twice the number of vibrations ; 
the second, the fifth of this octave, with three 
times the number of vibrations ; the third, the 
second higher octave, with four times the number of 
vibrations ; the fourth, the major third of the second 
higher octave, with five times the number of vibra- 
tions of the prime ; the fifth is the fifth of the second 
higher octave, or a minor third above the fourth 
partial, with six times the number of vibrations of 
the prime in the same time. Thus the partials go 
on, becoming generally fainter, to tones making 
seven, eight, nine, etc., times as many vibrations in 
the same time as the prime. We may also avoid 
using the word ' partials ' altogether, and call the 
harmonic constituents the first, second, third, etc., 



Helmholtz had forks constructed, the frequencies of 
which were in the order of a harmonic series, beginning 
with one having a pitch of 256 vibrations per second. 
These were then Ut 2 (f), Ut 3 (/), Sol 3 (/), Ut 4 (c"\ 
Mi 4 (/'), Sol 4 (/'), 7 (n nearly), Ut B ("'), etc. They 
were mounted on resonance boxes, by which the vol- 
ume of sound was much augmented. Thus any 
combination of the partials with the prime could 
be readily obtained by suitable bowing, and at the 
same time while the compound tone fell on the ear, 
the observer could effect an analysis by means of 
resonators. Since the invention of this method, 
Rudolf Konig has adapted his beautiful device of 
manometric flames, aided by the rotating mirror of 
Wheatstone, for the demonstration of the analysis of 
a compound tone. 1 

It will be evident that various combinations of the 
waves of the prime with those of the partials will 
produce varieties of wave form, and that the form of 
the resultant wave will be modified by the phase and 
the amplitude of the constituent waves. But we have 
seen that the ear can resolve musical tones into a 
series of partials, and that it behaves in accordance 
with the proposition advanced by Ohm, namely, that 
the human ear perceives pendular vibrations alone as 
simple tones, and resolves all other periodic motions of 
the air into a series of pendular vibrations, hearing 

1 For a figure of the apparatus, see ^M'Kendrick's Physiology, vol ii., 
p. 686. 

I 4 8 


the series of simple tones which correspond with these 
simple vibrations. 

The interesting question now arises, whether the ear, 
having to deal with waves varying almost infinitely in 
form, is differently affected by such waves, according as 
their form represents various modes of pressure (pushes 
and pulls) on the drumhead and conducting mechanism ? 
When we sound the harmonic series of forks from 
Ut to Ut 5 , we hear a rich harmonious sound, and we 
can analyse the sensation, and pick out the tone of any 
particular partial, more especially if it is slightly 
strengthened by a touch of the bow. By varying the 
order and intensity of the partials, we can produce a 
very large number of wave-forms, but the general 
character of the harmonious sound remains the same. 
In other words, waves may differ much in form, but 
if they contain the same harmonic constituents, the 
sensational effect will be the same. This would 
appear to indicate that the ear takes no cognisance 
of phase. Helmholtz invented a special apparatus 
to investigate this question. This costly apparatus 
was presented to him by King Maximilian of 
Bavaria. It consists of a harmonic series of forks, 
electrically driven, and so arranged that they can be 
sounded in any order and with various intensities, 
according to changes produced in the size of the 
orifices of their appropriate resonators. 1 The resona- 

1 A figure of the apparatus is given in M'Kendrick's Physiology, vol. 
ii., p. 691. 



tors may thus be put slightly out of tune, their 
resonance is weakened, and thus the phase is altered. 
Helmholtz stated the result as follows : ' Differences 
in musical quality depend solely on the presence and 
strength of partial tones, and in no respect on the 
difference in phase under which these partial tones 
enter into composition.' This statement has been dis- 
puted by Lord Kelvin, on theoretical grounds, and by 
Rudolf Konig, who has submitted it to the test of 
experiment ; but Lord Rayleigh remarks, regarding 
Konig's experiment, * the results are in harmony with 
the view that would ascribe the departure from Ohm's 
law, involved in any recognition of phase relations, to 
secondary causes.' J Physically, timbre must be due to 
the form of the vibration curve, otherwise telephoning 
would be impossible ; but the ear always analyses the 
curve into its constituents. 

With the view of establishing his theory of hearing 
on a firm basis, Helmholtz made a careful examination 
of the question of the existence of damping arrange- 
ments in the ear. Suppose tones are pouring into the 
ear in rapid succession, and that the effect of one tone 
has not died away before the influence of the next one 
is felt, musical effect would be disturbed. This would 
certainly occur if we executed a shake on a piano of 
eight or ten notes in a second, so that each note would 
be sounded four or five times. But it is well known 
that the sensation excited by such shakes is rough and 

1 Rayleigh, of. cit., vol. ii., p. 469. 


unpleasant, indicating, in the opinion of Helmholtz, 
' that the vibrating parts of the ear are not damped with 
sufficient force and rapidity to allow of successfully 
effecting such rapid alternation of tone. It is there- 
fore highly probable that a damping mechanism exists.' 

The next step was to attempt to explain how the 
cochlea, in which the nerve-endings exist in the form 
of the remarkable organ of Corti, can analyse tone, 
and with the development of this theory, however 
much it may have to be modified as time goes on, 
the name of Helmholtz will be imperishably con- 
nected. There are only three ways in which the nerve- 
endings may be affected. Either (i) small vibratile 
bodies may exist so as to transmit the pressures sent 
to the filaments of the auditory nerve, each vibra- 
tile body having a frequency period of its own ; or 
(2) individual nerve fibres may be directly excited 
by waves of a definite period, that is to say, there 
may be differences in the nerve fibres, so that they 
have a selective action ; or (3) the organ may be 
affected as a whole, all the nerve fibres being affected 
by any variations of pressures, and thus the power 
of analysis, which is admitted, would be relegated 
from the peripheral to the cerebral organs. 

The first hypothesis seems a priori to be probable, 
for the following reasons: (i) The existence of 
such bodies would give a natural explanation of many, 
if not all, of the phenomena ; (2) the evidence of 
comparative physiology points to gradually-increasing 


complexity in the structure of all the terminal organs 
of special sense, as if there arose a necessity for 
differentiation and discrimination in the effects of 
various kinds of stimuli ; and (3) investigations into 
the action of all the sense organs, such as those of 
touch and temperature in the skin, of light and colour 
in the retina, of taste in the tongue, and of smell in 
the olfactory region, all indicate specialization of 
function in the peripheral apparatus. 

Although the conception that vibrators exist in 
the cochlea flitted before the minds of Thomas 
Young, John and Charles Bell, and Johannes Miiller, 
it was first clearly put forward by Helmholtz. It 
may be shortly stated as follows : (i) In the cochlea 
there are vibrators, tuned to frequencies within the 
limits of hearing, say from 30 to 40,000 or 50,000 vibra- 
tions per second ; (2) each vibrator is capable of exciting 
its appropriate nerve filament or filaments, so that a 
nervous impulse, corresponding to the frequency of 
the vibrator, is transmitted to the brain, not corre- 
sponding necessarily as regards the number of nervous 
impulses, but in such a way that when the impulses 
along a particular nerve fibre reach the brain, a state of 
consciousness is aroused which does correspond with 
the number of the physical stimuli, and with the 
period of the auditory vibrator ; (3) the mass of each 
vibrator is such that it will be easily set in motion, 
and after the stimulus has ceased it will readily come 
to rest ; (4) damping arrangements exist in the ear, 


so as to quickly extinguish movements of the vibrators ; 
(5) if a simple tone falls on the ear, there is a pendular 
movement of the base of the stapes, which will affect 
all the parts, causing them to move ; but any part 
whose natural period is nearly the same as that of the 
sound will respond on the principle of sympathetic 
resonance, a particular nerve filament or nerve fila- 
ments will be strongly affected, and a sensation of a 
tone of a definite pitch will be experienced, thus 
accounting for the discrimination of pitch ; (6) intensity 
or loudness will depend on the amplitude of movement 
of the vibrating body, and consequently on the 
intensity of nerve stimulation ; (7) if a compound 
wave of pressure be communicated by the base of the 
stapes, it will be resolved into its constituents by the 
vibrators corresponding to the tones existing in it, 
each vibrator picking out its appropriate constituent 
and thus irritating its corresponding nerve filament, so 
that nervous impulses are transmitted to the brain, 
where they are fused in such a way as to give rise 
to a sensation of a particular quality or character, but 
still so imperfectly fused that each constituent, by a 
strong effort of attention, may be specially recognised. 
This last statement affords an explanation of the 
analytic powers of the ear. 

Now the structure of the ductus cochlearis, in 

which the nerve-endings exist, meets the demands 

of this theory. It is highly differentiated, and its 

parts appear suitable for executing independent vibra- 



tions. The minute size of the structures does not 
present any difficulty ; because, however minute the 
vibrators might be, if they had different periods, they 
must act in obedience to the same principles of 
resonance as larger bodies do outside the ear. In 
1863, Helmholtz was of opinion that the different 
degrees of tension in the arches of Corti indicated 
capacity for vibrating at different periods. Soon 
after, it was shown by Hasse that these rods do not 
exist in birds, animals presumably capable of appre- 
ciating tones ; and Hensen pointed out that the 
membrana basilaris, on which the rods rest, consisted 
of transverse fibres, which varied in length approxi- 
mately from -5iy 7 th f an inch, at the base of the cochlea, 
to -Vh of an inch at its apex. This led Helmholtz 
to suggest that it is probably the breadth of the 
membrana basilaris in the cochlea which determines 
the tuning. He pointed out that the membrane 
was in a state of tension transversely, while it has 
only little tension in the longitudinal direction, and 
that such a membrane had very different properties 
from that of a membrane which had the same tension 
in all directions. The membrane, in fact, behaves 
like a system of stretched strings, bound together by 
a semifluid substance. Each string or fibre would 
act independently of the others, and would be set 
into vibration by an impulse to the fluid in the scala 
vestibuli, corresponding to its period. Consequently, 
if a part of the membrane were called into action, one 


of its radial fibres, which corresponded to the exciting 
tone, would vibrate, and the vibrations would extend 
with diminishing strength on the adjacent portions of 
the membrane. Possibly some of the structures on 
the surface of the membrane might act as dampers. 
In this way the parts of the membrane near the base 
of the cochlea would be adapted for the higher, while 
those near the vertex of the cochlea would be suitable 
for the deeper tones. Corti's arches are, therefore, of 
secondary importance, serving either as supporting 
structures, or for transmitting vibrations of parts of 
the basilar membrane to the rows of hair cells placed 
on their backs. 

Helmholtz also discussed the question as to whether 
histological evidence as to the number of possible 
vibratile structures is such as will satisfy the demands 
of theory. He attempted to answer this question on 
the basis of E. H. Weber's statement, that practised 
musicians can 'perceive even a difference of pitch 
for which the vibrational numbers are as 1000 to 
1001,' or the ^\-th of a semitone, a smaller interval 
than that between two of Corti's arches, on the 
assumption that there are about 33^ for each semitone 
in each cochlea ; and he accounted for the apparent 
deficiency by the explanation, that if a tone came in 
between the pitch of two of the arches, 'it would 
set them both in sympathetic vibration, and the arch 
would vibrate the more strongly which was nearest 
in pitch to the proper tone.' This would also ex- 


plain how it is that when we listen to the syren, as 
its disc revolves faster and faster, our sensations go 
on, not by leaps and bounds, but continuously. Since 
the time when Helmholtz wrote, histological evidence 
has accumulated, the rods and arches of Corti, the 
fibres of the membrana basilaris, the hairs cells, and 
even the nerve fibres in each auditory nerve, have been 
counted, and it has been conclusively established that 
there is in the cochlea a sufficient number of possible 
vibratile masses to satisfy this theory. 

He then proceeded to examine the cause of con- 
sonance and dissonance, and to apply his theory in ex- 
planation. If we sound simultaneously two forks that 
are in unison, the waves coincide and one sound is 
heard ; but if the pitch of one of the forks is slightly 
flattened, the waves do not coincide, and there are 
maxima and minima. A rapid, rattling, beating sound 
will then be heard, as if there were individual thuds 
on the ear. If the forks are nearly the same in pitch, 
the beat, as it is termed, will be heard as a rising 
and falling in the intensity of the sound, and as the 
difference in pitch between the forks is increased, 
there is also an increase in the number of the beats. 
If such beats are few in number, so as to be readily 
counted, the sensation of waxing and waning is not 
disagreeable ; but if they are sufficiently numerous, 
it may be impossible to count them, and the sensation 
is disagreeable. Such a sensation is that of disson- 
ance. Helmholtz found the sensation to be most 


disagreeable when the ear is affected by about 33 
beats per second ; if they are more numerous, the 
sensation is rough and unpleasant. Further, even 
when the frequency of beats is much greater than 
the number of vibrations required to produce the 
sensation of a tone, the sensation is never uniform, 
but is of a rough, intermittent character. 

If now we sound an interval on an instrument 
giving forth compound tones, such, for example, 
as an octave, each note will have its corresponding 
partials ; and as these come closer and closer to- 
gether the higher they are in the series, it is 
clear that they may come within beating distance, 
and thus give a certain harshness to the sound. 
The beating distance may, for tones of medium pitch, 
be roughly fixed at a minor third ; this interval, 
of course, will expand for intervals in low, and 
contract for intervals in high ranges of the 
scale. Thus, the same interval in the lower 
part of the scale may give slow beats that are 
not disagreeable, while in the higher part it 
may cause harsh and unpleasant dissonance. Two 
given notes will produce this c beating ' harshness 
when the difference of their vibration number is 
about 70 or 80. Thus a minor third will sound 
pleasant in the higher ranges of the scale. There 
will be a slight roughness at medium pitches ; while 
in the lower ranges there will be harshness and 
possibly perceptible beating. On the other hand, if 


the interval be small, say a semitone, the beating, in 
the lower part of the scale, may be so slow as not to 
be disagreeable, whereas in the higher part it may 
cause harsh and unpleasant dissonance. The sensa- 
tional effect of beats then depends rather on the 
difference of the vibration numbers than on the interval. 
As a rule, the partials up to the seventh are beyond 
beating distance, but above this they soon come close 
together. In the neighbourhood of the tenth, the 
interval may be about a tone, of the sixteenth, a 
semitone, and still higher they come together so as 
to cause dissonance. This fact explains why intervals 
sound so harsh when produced by reeds, the sounds 
of which are rich in upper partials, and also the 
harsh but brilliant quality of intervals sounded on 
two trumpets. Intervals even when produced on 
instruments giving compound tones with few har- 
monic constituents, such as flutes, have still their 
own character. Helmholtz applied his theory with 
consummate skill, not only as an explanation of 
the quality of musical tones in many instruments, 
the human larynx included, but also of the satisfying 
character of certain musical intervals, as contrasted 
with the discordant character of others. Thus 
unison 1, minor third f, major third f, fourth f, fifth 
f, minor sixth f, major sixth f, and octave f, are all 
concords ; while a second -f- , minor seventh ^ and 
major seventh \ s , are discords. The smoothest in- 
terval is the octave, next the fifth, then the fourth, 


major third, and so on. What he did not explain 
is Why the sensation should be disagreeable when 
two portions of the membrana basilaris, sufficiently 
near, are thrown into vibration ? For some un- 
explained reason, if two nerve filaments sufficiently 
near are simultaneously stimulated, or if they are 
stimulated in the intermittent manner peculiar to 
beats, the sensation is disagreeable. Helmholtz 
contrasts it with that caused by a flickering light 
on the eye. There is, in listening to beats, always an 
effort at analysis, and it may be that this effort gives 
rise to a disagreeable sensation when the number of 
beats reaches a certain amount. 

While the theory explains the dissonance of in- 
tervals produced by instruments that are rich in 
partials, how does it apply to cases in which there are 
no partials, but only prime tones, as when the tones 
are produced by well-bowed tuning-forks and open 
organ pipes ? This question also was attacked by 
Helmholtz, and led to the examination of what he 
termed combination tones. If, for example, two 
forks representing a fifth are properly bowed, sound- 
ing the fork of lower pitch first and that of higher 
pitch afterwards, we may hear a weak lower tone, 
the pitch of which is an octave below that of the 
first fork. This is known as a combination tone. 
Such tones he divided into two classes differential 
notes, in which the frequency is the difference of the 
frequencies of the generating tones ; and summational 


tones, having a frequency which is the sum of those 
of the tones producing them. Then, when a fifth 
is sounded, the differential tone is an octave below the 
low note ; with a fourth it is a twelfth ; with a major 
third, two octaves ; with a minor third, two octaves and 
a major third ; with a major sixth, a fifth ; and with 
a minor sixth, a major sixth. Such differential tones, 
first heard by Sorge about 1740, are usually associated 
with the name of Tartini. Summational tones were 
discovered by Helmholtz. It is clear that there must 
be differential tones of several orders, according as 
they are produced between the generating tones them- 
selves, then between the differential tone and each 
of the generators, and so on. It is not difficult to 
detect differential tones, but this is not the case with 
summational tones. Helmholtz, who had a remark- 
ably acute and well-trained ear, heard them first with 
the polyphonic syren and the harmonium, and after- 
wards with organ pipes and tuning-forks. On the 
other hand, Hermann and others assert that they 
cannot hear these tones. There can be little doubt, 
however, that both kinds of combination tones may have 
an existence outside of, and quite independent of, the 
ear. Helmholtz states that c whenever the vibrations 
of the air or of other elastic bodies, which are set in 
motion at the same time by two generating simple 
tones, which are so powerful that they can no longer 
be considered infinitely small, mathematical theory 
shows that vibrations of the air must arise which have 
1 60 


the same vibrational numbers as the combination 
tones.' 1 Recently Riicker and Edser have demon- 
strated the objective existence of such tones. 2 Com- 
binational tones may, however, as Helmholtz clearly 
showed, be produced in the ear itself, because of the 
elastic asymmetry of the drum. 

The importance of these combinational tones in the 
theory of hearing is obvious. If the ear can only 
analyse compound waves into simple pendular vibra- 
tions, in a certain order, how can it detect combina- 
tional tones, which no doubt can be heard, and yet do 
not belong to that order ? For example, when the in- 
terval is harmonic (400, 500) the combined wave-forms 
make a wave of 100 of frequency, so that the ear, like 
Fourier's theorem, may easily pick out this tone ; but 
how will it deal with intervals of incommensurate 
numbers, such as 407, 483 ? Yet this combination 
tone of a frequency of 76 will be heard as distinctly as 
one arising from two tones having frequencies of 400 
and 500. This is still a great difficulty, as it cannot 
be said that experiments made by many others since 
the time of Helmholtz have removed it. Experiment 
shows that combinational tones are produced when the 
notes of intervals are sounded strongly on instruments 
like tuning-forks, whose notes are nearly simple tones, 
free from upper partials ; and that these combinational 
tones may produce beats with any of the generators, or 
among themselves ; and these beats, feeble as they 

1 Sensations of Tone, trans, by Ellis, p. 235. 2 Phil. Mag., April 1895. 


may be, produce that feeling of less and less con- 
sonance until we come to intervals that are truly 
dissonant. One might suppose that in the case of 
tones that abound in partials, combinational tones 
might be produced by the partials, and thus a new source 
of beats might lead to confusion and discord ; but 
theory shows that dissonance due to combinational 
tones, produced between partials, never occurs except 
when it has already taken place by the action of the 
partials among themselves. 1 

Closely connected with this subject is the investiga- 
tion of the cause of the quality of the human voice, 
more especially as to vowel tones. This also engaged 
the attention of Helmholtz, and it was treated by 
him in his usual masterly fashion. 2 Why should a 
vowel, spoken or sung, always have, even with the 
voices of different persons, the same quality, so that 
we have no difficulty in distinguishing A from E and 
E from O ? Bonders 3 was the first to show that the 
cavity of the mouth, as arranged for the giving forth 
of a vowel, was tuned as a resonator for a tone of 
a certain pitch, and that different pitches corresponded 
to the forms of the cavity for the different vowels. 
This he discovered, not by the use of tuning-forks, 
but by the peculiar noise produced in the mouth when 
the different vowels are whispered. The cavity of 

1 Sedley Taylor, Sound and Music. London, 1873. 

2 Gel. An*, d. k. bayer Acad. d. fTissensch, 1859. 

3 De Physiologic der Spraak klanken, 1870, s. 9. 



the mouth is then blown like an organ pipe, and by 
its resonance reinforces the corresponding partials in 
the rushing wind-like noise. Helmholtz adopted 
another method. To determine the pitch of the 
cavity of the mouth, considered as a resonance cavity, 
he struck tuning-forks of different pitches, and held 
them before the opening of his mouth. Then, the 
louder the proper tone of the fork was heard the 
nearer ' it corresponded with one of the proper tones 
of the included mass of air.' As the shape of the 
mouth could be altered at pleasure, according to the 
vowel to be emitted, it was easy to discover the pitch 
of the included mass of air for each vowel. He came 
to the conclusion that 'the pitch of the strongest 
resonance of the oral cavity depends solely upon the 
vowel for pronouncing which the mouth has been 
arranged.' He also found the same resonances for 
men as for women and children. He then carefully 
examined the form of the oral cavity for each vowel, 
and showed how very slight changes could account 
for the quality being slightly altered for different 
dialects. He also demonstrated that the tones of 
the human voice are adapted to the powers of the 
human ear. The ear, by its resonating powers, 
favours the development of these partials, especially 
the higher ones, which give a peculiar character to 
human tones. His theory as to vowel-tone is summed 
up in the following sentence : * Vowel qualities of 
tone consequently are essentially distinguished from 


the tones of most other musical instruments, by the 
fact that the loudness of their partial tones does not 
depend upon the numerical order, but upon the 
absolute pitch of those partials ; thus, if I sing the 
vowel A to the note E(>, the reinforced tone b"\> is 
the twelfth partial tone of the compound ; and when 
I sing the same vowel A to the note b'\>, the rein- 
forced tone is still b'\ but is now the second partial 
of the compound tone sung.' r He also endeavoured to 
reproduce, but with imperfect success, the tones of 
vowels by means of the same apparatus as he employed 
in the investigation of the influence of phase (p. 149). 
The theory of the absolute pitch of vowels, as advocated 
by Helmholtz, has met with great opposition, and to 
it is opposed the theory of relative pitch, but space 
forbids a critical examination of the subject. 2 

These important investigations, the results of which 
appeared from time to time, mostly after he had 
settled in Heidelberg, were collected by Helmholtz 
into his great book on Sensations of Tone, and formed 
Parts I. and II. Part III. is occupied with a discus- 
sion of the relationship of musical tones, the different 
principles of musical style in the development of music, 
the tonality of homophonic music, the music of the 
Greeks, consonant triads, keys, discords, the laws of 
progression, and the aesthetical relations of the whole 

1 Sensations of Tone, p. \"ji. 

2 Discussed in article on Vocal Sounds in Schaffer's Text Boot, vol. ii., 
p. 59, by M'Kendrick and Gray. 

I6 4 


subject. The mere enumeration of the subjects 
discussed will give one a faint idea of the breadth and 
fulness of this magnificent work. And yet even all 
this was only a part of the labours of Helmholtz in 
acoustics. As already mentioned, there is scattered 
throughout the volume, and in appendices, numerous 
examples of a mathematical treatment of the subject 
under discussion. In addition, we have papers on the 
motion of the strings of a violin, communicated, 
during one of Helmholtz's visits to his friend Lord 
Kelvin, then Professor William Thomson, to the 
Philosophical Society of Glasgow, on igth December 
1860. In this paper he fully discussed and repre- 
sented graphically the course of the vibration. 1 As 
already mentioned, he investigated mathematically 
the theory of damping, and calculated, for various 
intervals, the number of vibrations, after which the 
intensity of a free vibration is reduced to one-tenth. 
He estimated also the pitch of the partials produced 
immediately after a tuning-fork has been struck. He 
invented an electric interrupter, so as to produce an 
intermittent current in the best way and without 
making a noise by the production of sparks. He 
discussed the reciprocal relations of sounds, showing 
that a sound originating at one point is perceived at 
another point, even if there are obstacles between the 
two points, with the same intensity as if it originated 
at the last point and was perceived at the first ; just as 

1 See also Rayleigh's Theory of Sound t op. cit^ vol. i., p. 231. 
I6 5 


in optics, if one point can be seen from a second, the 
second can also be seen from the first. Sound shadows 
may thus be produced, but they are only partial, in 
consequence of the wave-lengths of sound being great 
in comparison with the sizes of ordinary obstacles. In 
connection with this subject, in 1860, he published an 
important paper, in which he examined the movements 
of the air in open organ pipes, and extended Green's 
well-known theorem, the chief application of which 
belongs to Statical Electricity. 1 He gave the 
correct theory for the open organ pipe. Lagrange, 
Daniel Bernoulli, and Euler assumed that at the open- 
ing the pressure could not vary with that of the 
surrounding atmosphere ; but Helmholtz showed that 
in ordinary cases the inertia of the air outside the pipe 
has the effect of practically diminishing its length. 
He also took into account the friction of the air 
against the walls of the tube, a point omitted by his 
predecessors. He also investigated some of the con- 
ditions under which the hammer of the pianoforte 
strikes the strings. He invented a vibration micro- 
scope for the examination of vibrating points on any 
body, say a violin string, so as to see the well-known 
figures of Lissajous. He established the mathematical 
relation of velocity and density in the propagation 
of small disturbances in gas or air. 

As already mentioned, he examined mathematically 
the laws that regulate the actions of resonators of various 

1 Rayleigh, op. >., vol. ii., p. 145. 

1 66 


forms and with variously-shaped apertures. He investi- 
gated the special mode of action of many musical instru- 
ments, and in particular, divided those having tongues 
into inbeating and outbeating. In the first case the 
passage is opened when the tongue moves inwards, 
that is against the wind, as happens in the clarinette. 
Lip instruments, such as the trombone, belong to the 
second class, the passage being open when the lips are 
moved outwards or with wind. 1 It may be said that 
the whole theory of the mode of action of tongue 
pipes is due to Helmholtz. He also gave a formula 
for the velocity of sound in narrow tubes. 

When Helmholtz first heard of the telephone, he 
remarked to Du Bois Reymond : c The invention 
seems so self evident, that I do not consider it necessary 
to advance a theory. Of course, I have for years gone 
to bed with Fourier's theorem in my head, and I have 
got up with it still there, so I must not judge others 
by myself.' His friend observes, that possibly it was 
on one of these nights that he was obliged to get up 
and lull his intellect by playing Bach's fugues on a 
magnificent grand piano presented to him by Messrs 
Steinway of New York in recognition of his services 
to music. On another occasion, he was interested 
and amused by the delightful experiment of causing a 
highly-trained vocalist to sing the vowels with the 
dampers off the strings, when of course they were 
returned little changed in quality. From the time 

1 Rayleigh, op. cit., vol. ii., p. 234. 
I6 7 


when Pythagoras is said to have discovered the arrange- 
ment of tones in an octave, by observing that the 
sounds of the blacksmith's hammer in the forge pro- 
duce a fourth, a fifth and an octave, and was then led 
to obtain harmonic proportion between the strings of 
the heptachord, all who investigate musical tones 
know that, although these are fleeting sensations, they 
depend physically on numerical relations between 
various kinds of movements ; but it was Helmholtz, 
more than any other philosopher, who examined the 
whole range of the phenomena, physical as well as 
physiological, and whose work will for generations 
remain an enduring monument to his genius. 




IT must be remembered that, both at Konigs- 
berg and Bonn, Helmholtz lectured on anatomy 
as well as physiology, and in Konigsberg he had 
general pathology in addition. This makes it more 
wonderful, that he should have been able to find 
time for so much physiological research, while it 
explains his familiarity with human anatomy. Even 
in the latter science a region one would suppose so 
harvested as not to leave a straw for the most indus- 
trious gleaner he found something to contribute to 
human knowledge. 

In 1856, his first year in Bonn, Helmholtz com- 
municated two short papers to the Medical Society 
of the Lower Rhine, both of an anatomico-physio- 
logical character. The first related to the anatomical 
structure of the thorax. He first showed that the 
ribs are attached behind to the vertebrae and in front 
to the sternum, and, during a state of rest, the 
anterior ends are on a lower plane than the posterior. 
When the ribs rise during inspiration, the sternal 


attachment moves forwards, and thus the ribs and 
their cartilages are submitted to torsion. Thus each 
rib-ring has a kind of elasticity like that of a hoop 
lying on a plane surface, and is stretched antero-pos- 
teriorly until it is slightly oval, and the thorax may 
be regarded as built up of such a series of rings. Each 
ring is in a position of stable equilibrium, until it is 
submitted to the muscular effort of inspiration, and 
to which it springs back by its elasticity. He also 
demonstrated the greater mobility of the upper part 
of the chest in the female than in the male. Finally, 
he took the view, that the external intercostals were 
inspiratory, while the internal had more to do with 
abdominal breathing. 

Somewhat later in the same year, he lectured on 
the muscles of the arm, and gave the result of obser- 
vations made both on the cadaver and on the living 
subject. Most of the actions described are now 
found in all anatomical books. He described speci- 
ally the movements of the clavicle and scapula. He 
then gave an account of the possible movements of 
the arm at the shoulder joint, supposing the arm to 
be extended at an angle of 45, with the flexor 
surface directed forwards. He accurately defined 
three axes of rotation, one horizontal from before 
backwards, a second parallel to the length of the 
upper arm, and a third perpendicular to the two 
former. As regards the process of supination of the 


forearm that is, moving it so as to direct the palm 
upwards, he is of opinion that the real supinator is 
the biceps, and that the so-called supinator longus 
is a real flexor. The strongest supination, when the 
arm is stretched, is brought about by the simultane- 
ous action of both biceps and triceps, and when the 
arm is flexed, then supination is brought about by 
the biceps alone. The action of the palmaris longus 
comes into play when the hand is made hollow, and 
it appears to protect the flexor tendons from the 
pressure of the folded skin. Finally, he showed that 
in the flexed position, the first phalanges can be 
rotated round their own axis by the interossei 
muscles, a movement which had not previously been 

The movements of the eyeballs were of great 
interest to Helmholtz, and he solved some of the 
difficult problems of single vision with two eyes. He 
had, as he himself remarked, a gift of seeing things 
in their geometrical relations, so that he was able to 
deal with questions of this nature with the greatest 
ease. In the year 1862, there appeared the first 
paper on the form of the horopter, that imaginary 
field in space, rays from any objects on which must 
fall on corresponding points of the two retinae, and 
consequently give rise to the sensation of a single 
image. The year 1863 saw two papers on the move- 
ments of the human eyes, giving an account of 


numerous ingenious experiments, and containing a 
mathematical treatment of the subject. In 1864, he 
delivered the Croonian Lecture to the Royal Society 
a famous lecture 'On the Normal Motions of 
the Human Eye in relation to Binocular Vision,' and 
this was followed in the same year by two papers 
on the horopter. In the following year, 1865, he 
published a paper on the Influence of the Orienta- 
tion of the Eyeballs on the Projection of the Retinal 
Pictures, another on Stereoscopic Vision, and a third 
on the Movements of the Eyeballs. At the Congres 
periodique internationale d'Ophtalmologie a Paris, in 
1867, he read a paper on Stereoscopic Vision and 
the Sense of Relief. He returned to the question in 
1878, after he became Professor of Natural Philosophy 
in Berlin, and even so late as 1881, in his sixtieth 
year, he published a note in the Philosophical Magazine 
on the same subject. 

It is somewhat difficult to give an account of the 
results of those researches in untechnical language, 
but it is only fair to Helmholtz to make the attempt. 
A picture of an external object is formed on the 
retina of each eye by the lens-like structures placed 
in front of it, in accordance with the laws of dioptrics. 
The two pictures, however, give the sensation of one 
object. Further, we can move the eyeballs so as 
to direct them to the object we wish to examine. 
Thus we can move them simultaneously up to the 
heavens or down to the earth, or to the right side 


or to the left. We can also look straight onwards, 
as when we gaze at the horizon, in which case the 
visual axes are parallel ; or we can look at a nearer 
object, converging the visual axes so as to cause 
them to meet at the object under examination. The 
effect of these movements is always to bring the 
images upon corresponding parts of the two retinae, 
and if they fall upon these, and not upon others, 
then there is single vision ; but if, from various 
causes, the images fall on other, or non-correspond- 
ing points, there will be double vision that is to 
say, we shall see two objects instead of one. The 
pairs of points that give rise to single vision were 
termed by Johannes Miiller corresponding points, 
and the assumption was that from any such pair of 
points similar nerve-fibres passed to the brain, and 
were possibly there so united as to give rise to the 
consciousness of a single object. 

Further, it has long been known that the retina 
of each eye is related to both sides of the brain, or, 
to put it conversely, each side of the brain is related 
to both eyes. If the optic nerves are traced back- 
wards, they are found to unite in the well-known 
optic commissure, and from the latter two great bands 
of fibres, termed the optic tracts, carry the nervous 
impulses to the brain. The whole of the nerve-fibres 
from the retina of each eye do not, however, cross or 
decussate in the commissure in the human mechan- 
ism, as was at one time supposed, but they do so in 


many animals, as, for example, in the pigeon. Thus 
a pigeon, in a sense, sees an object on its right side 
with its left brain, and vice versa^ and as the eyeballs 
in the bird are directed to the sides, it probably sees 
now with one eye, now with the other, and if objects 
are immediately in front or immediately behind its 
head, they probably form indistinct images, the bird 
does not see distinctly, and it therefore rotates its head 
with a well-known pert-like or quizzical action, so as 
to bring one eye to bear on the object. In man, how- 
ever, and in all the higher mammals, the decussation 
is not complete, and the arrangement is probably 
most complicated in man himself, so to meet the 
circumstances of his erect position with eyes in front, 
looking straight out upon the world. The fibres 
from the nasal side of each retina cross in the com- 
missure, while those from the temporal sides keep 
to their corresponding sides. Thus, in the eyes of 
a reader of this page, the nerves from the tem- 
poral side of the right eye keep on the same side 
in their course to the brain, but those from the 
nasal side cross over ; on the other hand, the 
nerves from the temporal side of the left eye 
also keep on the same side, and those from the 
nasal side cross in the commissure. The right 
brain is thus related to the temporal side of the 
right eye and to the nasal side of the left, and 
the left brain is related to the temporal side of the 
left brain and to the nasal side of the right. In 



this way the effect is as if the retinae were brought 
together, and the one were placed behind the other. 
In understanding vision with one eye there is no 
special difficulty. The globe might rotate round three 
possible axes, a vertical, a horizontal, and an antero- 
posterior. Movements are affected by four straight 
muscles (rect'i] and two oblique. The four straight 
muscles (rectus superior, rectus inferior^ rectus externus, 
rectus internus) arise from the back of the orbit, and 
pass forwards to their insertion in the front part of the 
eyeball, or its equator, if we regard the anterior and 
posterior ends of the globe as the poles. The two 
obliques (while one of them also originates at the back 
of the orbit) come as it were from the nasal side, the 
one goes above the eyeball and the other below, and 
both are inserted into the eyeball on the temporal side, 
the superior oblique above, and the inferior oblique 
below. The six muscles work in pairs. Thus the 
internal and external recti turn the eye round the 
vertical axis, so that the line of vision is directed to 
the right or left. The superior and inferior recti turn 
the eye round the horizontal axis, and thus the line 
of vision is raised or lowered. The oblique muscles 
turn the eye round an axis passing through the centre 
of the eye to the back of the head, so that the superior 
oblique lowers while the inferior oblique raises the 
visual line. Helmholtz was the first to discover that 
the oblique muscles, in certain circumstances, cause a 
slight rotation of the eyeball round the visual line 


itself. Normally, the superior rectus co-operates with 
the inferior oblique, and the inferior rectus with the 
superior oblique. 

The two eyeballs are also associated in their move- 
ments in the most exquisite manner, an association 
accomplished by a nervous mechanism which need not 
here be discussed. Suffice it to say, that when we 
look, say to the right side, the right external and the 
left internal recti work together, and when we look 
towards the left side, then there is harmonious co-opera- 
tion between the left external and the right internal 
recti. Again, the two superior recti act together if we 
look upwards, and the two inferior if we look down- 
wards ; if we look downwards pensively to the right 
side, the inferior recti of each eye, along with the 
superior oblique on the same side, and the internal 
rectus on the left side all come into play ; while, if we 
look to the left side, the corresponding muscles for 
that movement are brought into action ; and, finally, 
if we look upwards and to the right, then the superior 
recti contract, and are aided by the inferior oblique on 
the right side, and the internal rectus on the left ; 
while, if we assume the same attitude to the left, the 
superior recti again act, and are assisted by the inferior 
oblique on the same side, and the internal rectus on the 
right. As these muscles are innervated, in many cases, 
from opposite sides of the brain, it is clear that the 
cerebral actions must be of a very complicated char- 
acter. All these movements are under the control of 


the will, at least up to a certain point, but it was 
reserved to Helmholtz to show that there are other 
and slighter movements that are altogether involun- 
tary. Thus no one can voluntarily diverge the visual 
lines ; in other words, it is impossible voluntarily to 
cause simultaneous contraction of both external recti. 
Nor can we voluntarily rotate the eyeball round the 
antero-posterior axis, but here, again, slight involuntary 
movements may be made. We can thus turn the line 
of vision into every possible direction, but when its 
direction has been fixed, the position of the eye is also 
fixed, and is beyond our control. 

Helmholtz studied the subject by taking advantage 
of the method of Donders, which, by an ingenious 
device, he greatly improved. In this method, the 
apparent position of after-images produced by exhaust- 
ing the retina, say, with a red or green object, was 
compared with that of a line or fixed point gazed 
at with a new position of the eyeball. The ocular 
spectra soon vanish in this experiment, but a good 
observer can determine with great accuracy the coin- 
cidence of lines with the ocular spectra. Thus, after 
producing an after-image with the head in the erect 
position, the head may be placed into any inclined 
position, and if the attention is then fixed ion vertical 
lines, it can easily be seen whether the after-image 
coincides with the lines. As the after-image must 
remain in the same position on the retina, if it coin- 
cides with the vertical lines, it is evident there must 


have been a slight rotation of the eyeball. The coin- 
cidence always takes place, and thus it is proved that 
there is an involuntary rotation. Helmholtz also 
showed that this minute rotation had the advantage of 
enabling us to judge more correctly than we would 
otherwise do of the position of external objects. If 
the eyeball is thus rotated, the optic image will be 
slightly displaced, but if its new position is parallel to 
its former position, there is no apparent motion ; but 
if the rotation is only through infinitely small angles, 
the eye may move round axes perpendicular to the 
visual line, and thus the optic images will remain 
parallel to their first positions. Now Listing had 
already discovered the law that, in the so-called third 
positions of the eyeball, it rotates, not round an 
antero-posterior axis, but round axes perpendicular to 
the visual line. Helmholtz demonstrated the truth of 
this law, and, finally, by the calculus of variations, 
solved the mathematical problem. 

He next proceeded to investigate single vision with 
both eyes. The two fields of view that seem to be 
superposed are the corresponding or identical points of 
Johannes Miiller. But we see things in relief; this 
may also be done with Wheatstone's stereoscope, and 
in neither case can we perceive the duplicity of the 
images. Helmholtz showed, however, that if we sup- 
pose two objects, say two stereoscopic pictures, to have 
vertical lines or meridians that are not in reality truly 
vertical, but each set slightly inclined to the right or 


left, and if we look at these through a stereoscope, the 
'squinting' lines accurately coincide, thus showing 
that in double vision it is not the real vertical meridians 
of the fields of view that coincide, but the apparently 
vertical meridians. The horizontal meridians always 
coincide. Thus while the retinal horizon is horizontal 
for both eyes, the apparently vertical meridians are not 
perpendicular to it, as had been hitherto supposed, but 
they diverge at their upper extremity, at an angle of 
from 2 22' to 2 33'. Corresponding points are 
therefore equally distant from each retinal horizon, 
and from each apparently vertical meridian. This 
led to the examination of the true geometrical form 
of the horopter, by which is meant the locus of 
those points of space which are projected on cor- 
responding retinal points, and he found that it is 
generally a line of double curvature produced by the 
intersection of two hyperboloids, that is to say, it is 
a twisted cubic curve formed by the intersection of 
two hyperboloids which have a common generator, 
and in some special cases it is a combination of two 
plane curves. ' The curves pass through the nodal 
points of both eyes. An infinite number of lines 
may be drawn from any point of the horopter so as 
to be seen single, and these lines lie on a cone of the 
second order whose vertex is the point. Helmholtz 
also showed that when we look at the horizon, the 

1 The mathematical demonstration is given in HeatKi Geometrical 
Of tics, p. 233. Cambridge, 1887. 

I 79 


horopter is really a horizontal plane passing through 
our feet, thus warranting the name first given to it by 
Aguilonius in 1613. The horopter in this case is the 
ground on which we stand. Experiments show 
* that the forms and the distances of these objects 
which are situated in, or very nearly in, the horopter, 
are perceived with a greater degree of accuracy than 
the same forms and distances would be when not situ- 
ated in the horopter.' 

The investigation of this subject led Helmholtz to 
the invention of the telestereoscope, an instrument 
containing a combination of prisms, by which two 
images of distant objects can be seen as if the eyes 
were widely separated in the head. Consequently, 
combination takes place, and the objects are seen in 
relief. Further, Helmholtz, in his later researches, 
came to the conclusion, that the apparent fusion 
of two retinal images cannot be explained by 
any anatomical arrangement, but that it is due 
to a mental act. Briicke's notion, that the per- 
ception of solidity might be due to sensations excited 
by muscular contractions causing convergence of the 
visual axes, is negatived by Dove's observation, 
that the illusion of stereoscopic pictures is also pro- 
duced when they are illuminated by the electric 
spark, lasting less than the ^V^th of a second, 
and in this short time there cannot be the 
slightest movement of the eyeballs. The study of 
stereoscopic lustre, also first noticed by Dove, pro- 


duced when one stereoscopic picture is white and the 
other grey, shows also that the impressions on the two 
retinae are not combined, in this case, into one sensa- 
tion. There is a rivalry of the fields of visions, best 
seen in the rivalry of colours, when one stereoscopic 
picture is red and the other blue. A true combina- 
tion purple is not produced, but there is a peculiar 
'sheen,' and the red at one moment has the pre- 
dominance, and the instant after it is the blue. 

The whole of this beautiful research is a good 
illustration of the method of Helmholtz. Complicated 
as the movements of the eyeball apparently are, they 
become simple when we consider that they are just 
the movements that are necessary to see single objects 
with two eyes. It was this simple principle that 
guided Helmholtz. Only those, however, who have 
read the chapters on the subject in his Physiological 
Optics can form a conception of the amount of work 
expended upon it. The bibliography alone is a model 
of literary research. 

In 1869, he investigated the cause of hay-fever, a 
troublesome affection to which he was susceptible, 
and which interfered much with his pleasure during 
holiday time. He announced the discovery in a letter 
to Binz, who secured its insertion in Virchow's Archiv 
fur pathologische Anatomie. Helmholtz found in the 
mucus of the nasal secretions of persons affected by 
this disease micro-organisms of a vegetable nature, 


and having observed the researches of Binz on the 
poisonous action of sulphate of quinine on such organ- 
isms, he applied to the mucous membrane of the 
nostrils a solution of one of the salt in eight hundred 
of water, with almost instant relief. This thera- 
peutical measure was first carried out in 1867 j it 
was often repeated, and, in 1872, Helmholtz told Binz 
that he was quite cured. To medical men Helmholtz's 
descriptions of the disease will be interesting, and 
possibly it shows that he might have made an excellent 
clinical observer. 1 

'An extraordinary violent sneezing then sets in, 
and a strongly corrosive thin discharge, with which 
much epithelium is thrown off. This increases, after 
a few hours, to a painful inflammation of the mucous 
membrane and of the outside of the nose, and excites 
fever, with severe headache and great depression, if the 
patient cannot withdraw himself from the heat and the 
sunshine. In a cool room, however, these symptoms 
vanish as quickly as they come on, and there then only 
remains for a few days a lessened discharge and soreness, 
as if caused by the loss of epithelium. I remark, 
by the way, that in all my other years I had very 
little tendency to catarrh or catching cold, while 
the hay-fever has never failed, during the twenty-one 
years of which I have spoken, and has never attacked 
me earlier or later in the year than the time named.' 

1 Nature, vol. x., p. 26, May 4, 1874. Letter to Prof. Tyndall from 
Prof. Binz of Bonn. 




T T ELMHOLTZ occupied the Chair of Physiology 
A A in Heidelberg from 1859 to 1871, when he 
was placed in the chair of Magnus in Berlin. In 
Heidelberg he lectured upon physiology only, and he 
had thus greater leisure to devote to physical and 
physiological research. During this period of eleven 
years, he contributed nearly sixty papers, and, of these, 
twenty-four were on physical questions. Even this 
statement, however, does not give full expression to 
his intellectual activity, for the great work on Physio- 
logical Optics made its appearance in parts in 1856, 
1860, and 1867, and the equally valuable book on 
Sensations of Tone was published in 1863, both books 
full of the results of special research. He also lectured 
at the Royal Institution of Great Britain on the 
Conservation of Energy in 1864, and, from time to 
time, he delivered, and in 1865 and 1871 published, 
some of those admirable popular lectures that represent 
the highest class of that form of literature in any 



Indeed, it may be said that this was a transitional 
period in the life of Helmholtz. A born physicist, as 
he himself often said, he more and more occupied his 
mind with some of the deepest problems in this depart- 
ment of science. From 1866, when he published a 
well-known paper on the sounds emitted by a contract- 
ing muscle, and 1867, when the elaborate investiga- 
tion of the bones of the ear appeared, he published little 
that was purely physiological, and he devoted himself 
almost entirely to physics. As he felt that this was 
his vocation, he left physiological research to a great 
extent in the hands of pupils, assisting and counselling 
them in their work, sometimes co-operating in publica- 
tion, as when, in 1867 and 1870, he issued the results 
of a research by himself and his pupil Baxt on the 
velocity of the nervous impulse in the motor nerves 
of man. 

On the death of Magnus in 1871, it was felt that 
only one of two men in Germany could take his place 
as Professor of Physics in the University of Berlin. 
Du Bois Reymond, who was then Rector of the 
University, was empowered by von Miiller, the 
Minister of Education, to go to Heidelberg and 
persuade Kirchhoff, one of the founders of spectrum 
analysis, or Helmholtz, to accept the vacant chair. 
The Government of Baden would not allow KirchhofF 
to leave, and so the chair was offered to Helmholtz. 
This he accepted with some reluctance, for he loved 
the wooded hills around Heidelberg and the old 


romantic town, but no doubt also he yielded to the 
entreaty of his friend with pride and satisfaction. 
He had now raised himself to the position of being 
the first physicist in Germany, and his fame extended 
throughout the scientific world. The young army 
surgeon, who astonished his friends twenty-four years 
before by writing the ' tract ' I (as it is modestly called 
by himself and by Clerk Maxwell), was now, at the 
age of fifty, in a position where he could give his 
undivided attention to his first love physical science 
a position, also, specially suited to his inclination 
and talent. 

The years rolled on till 1887, when another great 
change took place in the career of Helmholtz. His 
life-long friend, Werner von Siemens, the electrician 
and man of affairs, founded a great Physico-Technical 
Institute at Charlottenburg, near Berlin, and Helm- 
holtz was chosen as its first director. The object 
of this institute was (i) to deal with costly and diffi- 
cult scientific investigations not likely to be under- 
taken in any ordinary physical laboratory, such as 
those relating to standards of measurement ; and 
(2) to undertake special technical procedures, includ- 
ing the testing of all kinds of thermometers, con- 
structed on the most approved principles, the testing 
of aneroids, mercurial barometers, the examination of 
all kinds of instruments for electrical measurements, 
the examination of photometric instruments, and the 

1 Die Erhaltung der Kraft ; or, The Conservation of Energy. 
I8 5 


establishment of a unit of light ; the testing of tuning 
forks, the construction of universal screws, and, in- 
deed, all methods and instruments having to do with 
higher technical research and instruction. The In- 
stitution had at least one point of contact with the 
medical profession, as we find that 25,000 clinical 
thermometers were tested and stamped during the 
first three years. 

Werner von Siemens, whose admiration for the 
talents of his friend was boundless, wished Helmholtz 
to be entirely relieved from teaching, so as to leave 
his energies freedom to work in the higher regions of 
research, but circumstances made it important that 
Helmholtz should retain his chair. This he did till the 
year of his death in 1894, lecturing during the session 
twice a week on such special subjects as the mathe- 
matical theory of vibrations, electrodynamics, and the 
mathematical developments of light and sound. In 
the Institute, with a staff of fifty officials, Helmholtz 
had now to undertake much administrative work, and 
he performed this part of his duties with the same 
zeal and thoroughness that had characterised his whole 
life. It was certainly work different from that to 
which he had been accustomed, far removed, for 
example, from the fascinating study of sense-percep- 
tions, but it was public work to which Helmholtz 
attached great importance. His mind still soared into 
the loftiest regions of scientific thought, and some of 
his most advanced papers on mathematical physics 


appeared during the last ten years of his busy life. 
Further, he was cheered by the social brightness of a 
happy home life. In 1861, Helmholtz entered upon 
a second marriage with Miss Anna von Mohl, of a 
Wiirtemberg family of high social position. This 
lady became the worthy helpmate of so great a man ; 
by her side many of his immortal works were created, 
and their home was the centre of a brilliant social, 
artistic, and intellectual circle. Two children were 
born of this marriage. The elder son, Robert, died 
in 1889 at a comparatively early age, after he had 
given promise of having inherited some of the apti- 
tude for mathematical and physical research which 
so distinguished his father ; while the daughter knit 
together the houses of Siemens and Helmholtz by 
marrying the son of Werner von Siemens. The loss 
of his son was deeply felt, and it is said that Helm- 
holtz never recovered from the blow. Thus the 
brilliancy of his career was dimmed by his experience 
of sad events that come to all alike. 

During the last twenty-three years of his life, Helm- 
holtz devoted his energies entirely to the investigation 
of physical problems. The only exception to this 
statement is, that questions of a philosophical nature, 
which will be dealt with in a future chapter, also 
engaged his attention. To these questions he was 
led by the consideration of his theory of knowledge, 
founded on the thorough examination he had made 
into the nature of sensation and perception. In 


physical science he occupied himself almost wholly 
with profound discussions, of a highly mathematical 
character, into hydrodynamics, or the motions of 
fluids, whether liquid or aeriform ; into the nature of 
the ether and its relations to electrodynamics and 
thermodynamics ; into some of the phenomena of 
light ; and into principles concerned in the move- 
ments of atoms and lying at the root of mechanics. 
He also applied his profound knowledge of the more 
hidden physical movements to an explanation of 
chemical phenomena, more especially as to the rela- 
tion of these phenomena to the law of the conser- 
vation of energy ; and, finally, he passed into the 
region of the physics of certain meteorological pheno- 
mena, such as the nature of clouds. It is remarkable, 
as showing the vigour of his intellect, that he was 
creative up to the year of his death. Year after 
year he ventured higher and higher in the choice of 
problems on which to exercise his powers, and 
although he gave the results in his ordinary lectures, 
the number of pupils, and indeed of physicists, 
throughout the world, who could follow him, became 
fewer and fewer. 

Helmholtz had transcendent gifts as a mathema- 
tician. We have it on the authority of Du Bois 
Reymond, that not long before he wrote the tract 
on the conservation of energy, his younger friends 
were astonished at his mathematical attainments and 
at the width of his reading of the more famous 

1 88 


mathematical treatises. Had he chosen pure mathe- 
matics as his future field of labour, there is no doubt 
he would have won distinction here as elsewhere, but 
he always subordinated mathematics to the investi- 
gation of physical questions. He did not revel in the 
deduction of the purely abstract truth of geometry 
and algebra, but the abstract propositions and methods 
of mathematics were to him a means to an end, and 
he knew that mathematical analysis is only a rigid 
system of logic in which wrong premises may conduct 
more surely to a wrong conclusion. He therefore 
always endeavoured, if possible, to obtain data on 
which to base his calculations. Yet no one knew 
better that mathematics will win victories where 
experiment may be beaten, and that, to use the 
words of Lovering, * mathematical analysis, with its 
multitudinous adaptations, is the only key which will 
fit the most intricate wards of the lock guarding 
the treasury of science.' Thus, in a review of Vol. 
I. of Lord Rayleigh's Theory of SoundJ Helmholtz 
remarks : * Without the resources of mathematics, a 
really complete insight into the casual connection of 
the phenomena of acoustics is altogether impossible.' 
Again, he says : c We see in mathematics the logical 
activity of our mind in its purest and most perfect 
form, and while we are conscious of the toil and of 
the difficulty in forming abstract ideas, we have at 
the same time confidence in the security, influence, 

1 Nature, vol. xvii., p. 238. 


and fruitfulness of such mental labour.' The same 
is true of all departments of physics, and especially 
of those departments that deal with the hidden pro- 
perties of matter. It need scarcely be said that the 
pure mathematicians, men always of the first mental 
calibre, are forging the tools with which the physicists 
of the future will attempt to solve still more recondite 
problems than those that at present engage their atten- 
tion. When the monumental labours of such men 
as William Rowan Hamilton, Joseph Sylvester, and 
Arthur Cayley are looked at from this point of view, 
it will be seen that advanced mathematics does not 
consist merely of a series of mental gymnastics, but 
that the subject is of the highest practical importance, 
because it leads the way to an adequate conception 
of the phenomena in the physical universe. 

' O wretched race of men, to space confined ! 
What honour shall you pay to him whose mind 

To that which lies beyond hath penetrated ? 
The symbols he hath formed shall sound his praise, 
And lead him on to unimagined ways, 

To conquests new in worlds not yet created.' r 

It may be said, in the words of Helmholtz's greatest 
pupil, Heinrich Hertz, that the ultimate function of 
science is to formulate the problems of nature mathe- 
matically, and thus bring the logical consequences of 
thought into harmony with the phenomena happening, 

1 Linet written by Clerk Maxwell with reference to Cayley. 


or appearing to happen, in the outer world. When 
this has been accomplished, then all physical problems 
will be solved. Even now the mind can imagine 
such a being as arose to the mental vision of Laplace, 
thus described by Helmholtz himself: ( An intelli- 
gence which at any given instant should know all 
the forces by which nature is urged, and the respec- 
tive situation of the beings of which nature is com- 
posed ; if, moreover, such a mind were sufficiently 
comprehensive to subject these data to calculation, 
such an intelligence would include in the same for- 
mula the movements of the largest bodies of the 
universe and those of the smallest atoms. Nothing 
would be uncertain to such an intelligence, and the 
future no less than the past would be present to 
his eyes.' 

G. H. Wiedemann, 1 a contemporary of Helmholtz, 
aptly points out that he had two methods of looking 
at things, which he used according to the nature of 
the problems treated and their state of development, 
(i) In his earlier works, and in a few of the later 
ones, Helmholtz starts from general principles of 
dynamics, or from general differential equations, 
and attains results without special assumptions as to 
the structure of matter, or the nature of electricity. 
Examples of this method are afforded by the tract 
on the conservation of energy, by his examination 

1 Introduction to Helmholtz's f^lisenschafdiche Abhandlungtn, vol. 
Hi. Leipzig, 1895. 


of Weber's statement of electrical action at a distance, 
and by his papers on hydrodynamics ; (2) later works, 
such as those on electrolysis and on the more hidden 
movements implied in his theory of cyclic systems, 
show Helmholtz taking advantage of molecular hy- 
potheses. In his appreciation of Helmholtz's labours, 
Wiedemann gives this little personal touch to the 
picture that seems to bring the man before us : c Helm- 
holtz did with nature just what he did in looking at a 
picture or listening to a piece of music. He looked 
for a scientific foundation and analysed his feelings. 
The waves of the sea breaking on Cape d'Antibes 
roused his scientific spirit. From the relative velocity 
of the wind and the number of waves on the surface 
of the sea, he drew conclusions as to the arrangement 
of the clouds, and these were submitted to mathe- 
matical investigation. 1 

An exhaustive account of the physical researches of 
Helmholtz would far exceed the limits of this work ; 
and indeed it is almost impossible to give the results 
in untechnical phraseology without running the risk 
of being much misunderstood, and yet no true notion 
can be formed of this great Master in Medicine without 
recognising that it was in physical research, both in 
the animate and inanimate world, that he truly ex- 
celled. In this department the labours of his life may 
be summed up under six heads: (i) On the Con- 
servation of Energy ; (2) On Hydrodynamics ; (3) On 

1 Wiedemann, of. cit. xxxi. 
I 9 2 


Electrodynamics and Theories of Electricity ; (4) 
On Meteorological Physics ; (5) On Optics; and (6) 
On the Principles of Dynamics. 

I. On the Conservation of Energy. 

This has already been dealt with in Chapter V., and 
it has been shown that Helmholtz played an important 
part in formulating, from a mathematical standpoint, 
this great principle. 1 In the labours of his after 
life it was his guiding star. It pointed out the path 
of research, while it was the final test to which all 
theories were submitted. The tract not only estab- 
lished the theory from general principles, but it con- 
tained illustrations of an electrical character to which 
reference is still made in all discussions of the subject. 2 
In later researches he verified Lord Kelvin's doctrine 
of the dissipation of energy that only certain forms of 
energy can be completely changed into others a 
result in accordance with the second law of thermo- 
dynamics, which asserts that it is impossible, by the 
unaided action of natural processes, to transform any 
part of the heat of a body into mechanical work, 
except by allowing heat to pass from that body into 
another at a lower temperature. 3 This is the modern 

1 See Tail's Sketch of Thermo-dynamics, p. 68. Edinburgh, 1877. 

2 Clerk Maxwell. Electricity and Magnetism, vol. ii., p. 176. Ox- 
ford, 1873. 

3 Clerk Maxwell. Theory of Heat, p. 153. London, 1872. 



basis of Carnot's principle, and was first given in a 
somewhat less definite form by Clausius, who pub- 
lished his work soon after he had reported to the 
Physical Society of Berlin on Helmholtz's paper on 
the Conservation of Energy. Helmholtz, in 1883, 
also applied the principle to chemical phenomena. 1 
Starting from the fact that heat never passes from 
a colder to a warmer body without making the 
former colder and the latter warmer, and that all 
the energy which already exists as heat cannot be 
converted into visible external energy, he drew a 
great distinction between free and restricted energy. 
Thus the energy of the chemical changes in a galvanic 
element cannot, without further chemical changes, 
become a measure of the electro-motive force ; only 
a small part of the energy appearing as electrical 
energy. In all chemical changes in which heat 
appears, all the energy does not appear as heat, but 
a portion is still locked up in the chemical compounds. 
Thus the internal energy of a system may be said to be 
composed of free and restricted energy, of which the 
former can be changed into work while the second 
appears as heat. He thus gives us a glimpse into the 
dynamics of chemical processes, and especially those of 

2. On Hydrodynamics. 
Helmholtz published eight important papers on the 

1 IVusenschaftL Abhandlungen, Bd. iii., s. 92. 


movements of fluids. It was in 1858, while he was 
Professor of Physiology in Bonn, that he published his 
famous paper on Vortex Motion. 1 The paper was 
adversely criticised by the French mathematician 
Bertrand ; and, in 1868, Helmholtz replied in such 
a manner as to silence controversy, in three papers 
published in the Comptes Rendus de F Academic des 
Sciences de Paris. In the same year appeared a valu- 
able paper on the discontinuous motion of fluids ; 
in the following year, one on stationary streams ; 
and, in 1873, an important theoretical paper, in 
which is developed a theorem with respect to geo- 
metrically similar movements of fluid bodies, and their 
application to the mechanical problem of steering 
balloons. There are also remarks on the mechanism 
of flight. Undoubtedly the most important of these 
contributions to science is that on vortex motion, 
an investigation that had baffled such great mathe- 
maticians as Euler and Lagrange, on account of 
inherent difficulties. Stokes first pointed out the 
real distinction between vortex and non-vortex 
motion ; but it was reserved for Helmholtz to dis- 
cover the fundamental laws which govern vortex 

A fluid differs from a solid body in that its particles, 
within certain limits, can move relatively to one 
another. Practically, even in the most mobile or 
least viscous of fluids, relative motion of contiguous 

1 Wisfemchaftl. Ablumdlungen, Bd. i., s. 101. 


parts is more or less gradually destroyed by virtue of 
viscosity or fluid friction. In a viscid fluid there is 
a great internal friction ; and from this extreme case 
we can pass by gradations to fluids of less viscosity 
until we arrive at a very mobile fluid like sulphuric 
ether. This suggests the abstraction of a perfectly 
frictionless fluid, in which there is no tangential stress 
between elements sliding past one another. The 
greater part of the theory of hydrodynamics deals with 
such an ideal fluid, for the simple reason that our 
mathematical methods are insufficient to attack the 
general problem of the motion of a viscous fluid. Al- 
though no known fluid is even approximately friction- 
less, nevertheless the study of the ideal frictionless fluid 
leads to important results and must ultimately enable 
us to understand better the effects of fluid friction. 
In 1858 Helmholtz investigated, mathematically, the 
laws of vortex motion in a frictionless fluid. In 
addition to the very remarkable theorems in hydro- 
dynamics, to which Helmholtz was led and on which 
Lord Kelvin and others have based whole theories of 
the ultimate constitution of matter, the investigation 
has another important side. The mathematical for- 
mulas are identical with certain formulae in electro- 
magnetism, so that, as Helmholtz himself pointed out, 
there is a striking analogy between the two apparently 
distinct classes of phenomena, hydrokinetics and electro- 
kinetics. Indeed all mechanical models that aim at 
explaining the reciprocal relations of electricity and 


magnetism require rotating elements ; and vorticity of 
some kind seems to be an essential feature of electro- 
magnetic action. 

Wherever in a fluid vortex motion exists, there is 
rotation of the smallest imaginable particle about some 
axis. Starting from this conception, which Stokes was 
the first to describe clearly, Helmholtz proceeds to 
investigate the forms and behaviour of vortices. A 
vortex line he defines as a line drawn through the 
fluid in such a way that its direction at any point is 
the axis of rotation of the element at that point. A 
vortex filament is part of the fluid marked off from 
the surrounding fluid by drawing the corresponding 
vortex lines through all points of the circumference of 
an infinitely small plain area. Thus each vortex 
filament may be imagined to be shut off from the 
surrounding fluid by a thin layer or mantle of vortex 
lines. Vortex lines form closed curves in a finite 
fluid ; and vortex filaments form closed filaments or 
rings, simple or knotted. The simplest type of a 
vortex ring is a circular anchor ring, every element 
rotating round the circular axis. Such a vortex ring 
advances through the fluid in the direction of motion 
of the elements on the inside of the ring. An ordinary 
smoke-ring shows the essential nature of the motion 
very well. If two vortex rings have the same axis 
and the same sense of rotation, and if they both 
advance through the fluid in the same direction, 
the first ring, a, will widen, and suffer retardation, 


and the second, , will become narrower, and suffer 
acceleration, b ultimately overtaking a, and, under 
favourable conditions, passing through it. Then they 
will separate and again follow each other, but b will 
widen, and a contract, until a will pass through b. 
Thus the vortex rings will pass alternately through 
each other. On the other hand, if the coaxial rings 
have equal radii and equal rotational movements, but 
in opposite senses, they will approach each other 
and suffer distension, and this mutual approach and 
simultaneous spreading out will go on indefinitely 
until the rings are infinitely close and infinitely 

In an incompressible frictionless fluid rotatory 
movements can neither originate nor disappear ; the 
vorticity, or product of any section of the ring and 
the speed of rotation, then is an unchangeable 
quantity. As they move in the surrounding fluid 
they are always composed of the same particles. 
Thus the vortex rings have perpetuity. They may 
jostle against each other and undergo endless 
changes of form, but they cannot be broken or 
dissolved. They have the indestructibility which is 
believed to belong to the ultimate constituents of 
matter. Lord Kelvin made Helmholtz's investi- 
gation the basis of the splendid hypothesis, that the 
atoms of matter are composed of minute vortex 
rings in the ether, and he worked out in detail 
the analogy between such rotational movements and 


electro-magnetic phenomena. Even this idea as to 
ether being the basis of matter seems to have lurked 
in the all-embracing mind of Newton, for he says : 
'Thus, perhaps, may all things be originated from 
aether.' r In later years, Helmholtz accepted Lord 
Kelvin's idea and contributed remarkable mathematical 
papers in its support. The element, according to this 
conception, is neither a solid atom, nor a mass of 
atoms, but a whirl in a fluid ether. The molecules 
of a particular element have one invariable and 
unchangeable mass ; when the substance is incan- 
descent, its molecules are vibrating, and emit the 
same kind of light, being tuned, as it were, to 
definite pitches. As Levering said : * The music of 
the spheres has left the heavens and condescended to 
rhythmic molecules. There is no birth or death or 
variation of species. If other masses than the precise 
ones which represent the elements have been elimin- 
ated, where, asks Clerk Maxwell, have they gone? 
The spectroscope does not show them in the stars or 
nebulae. The hydrogen and sodium of the remotest 
space is in unison with the hydrogen and sodium or 
the earth.' 2 Finally, the theory of vortex motions 
has made it possible to understand in some measure 
the transmission of magneto-electric effects through an 
intervening medium, and it has also helped to dispel 

1 Letter to the Secretary of the Royal Society, Henry Oldenburg, 
Jan. 1676. (Hat. of Royal Society, by T. Birch, vol. iii., p. 250). 

2 Joseph Levering. Address to American Association for Advancement 
of Science. Hartford, Aug. 14, 1874. 

I 99 


the fiction of action at a distance. Some idea may 
be formed of the possible variety of forms of vortex 
atoms by simply looking at the illustrations of Pro- 
fessor Tait's remarkable paper upon Knots. 1 

1 Scientific Papers, vol. i., p. 273. 




IN 1868, Helmholtz pressed farther the analogy 
between the equations of fluid motion and those 
of electricity and heat in a paper on movements in 
discontinuous fluids. He also endeavoured to account 
for certain discrepancies that exist between theory 
and experiment. He found that such discrepancies 
are greatest in cases where the current enters a wide 
space through an opening having sharp edges. In 
such circumstances, discontinuity of the fluid occurs ; 
it is, as it were, torn asunder, and a surface of separa- 
tion is formed with rounded edges ; rupture will only 
occur with increased velocity of the fluid. These 
investigations have also a practical bearing on the 
theory of the flow of water through cylindrical pipes, 
and on the origin of rotational movements. In this 
memoir, also, he showed the applications of several 
formulae to electricity, in which the co-ordinates are 
expressed as functions of the potential and its con- 
jugate functions. For example, he discussed the case 


of an electrified plate of finite size parallel to an infinite 
plane surface connected with the earth. 

It was important for hydrodynamical theories to 
determine with exactitude the internal friction of 
fluids. Two important researches were undertaken. 
In one, along with G. von Piotrowski, Helmholtz 
observed the friction that occurs at the borders of 
the fluid where it touches the surrounding medium. 
A globe of metal, having a polished and gilded 
interior, was filled with various fluids and swung 
round a perpendicular axis, while the delay in the 
vibrations or movements at the border was observed 
and measured by means of a mirror reflecting a beam 
of light into a telescope. This method was similar 
to that previously employed by Bessel, whose obser- 
vations and mathematical deductions are fully dis- 
cussed. In long thin tubes, as was shown by 
Poiseuille, the upper layer of fluid adheres firmly to 
the walls of the tube, but this was shown not 
to be the case with the polished globe when filled 
with water, though it was true as regarded alcohol 
and ether. The other research dealing with ques- 
tions regarding friction was mathematical, and com- 
pleted the theory of stationary or static streams in 

The theorem as to the geometrically similar move- 
ments of fluid bodies, issued in 1873, made it possible 
to draw some practical conclusions regarding the 
steering of balloons, with which the behaviour of a 


ship was compared and contrasted. Helmholtz sug- 
gested cigar-shaped balloons. The conditions of flight 
also arrested his attention. He was of opinion, on 
theoretical grounds, that the great condor of the 
Andes has probably reached that limit of size at 
which a bird can still soar in the air by the action 
of the muscles of its wings ; and he despaired of 
man ever being able to lift himself from the ground 
by muscular action alone, however ingeniously applied. 

3. On Electrodynamics and Theories of Electricity. 

Electrical phenomena of all kinds irresistibly 
attracted Helmholtz throughout his whole life, and 
his works show, from the tract on the conservation of 
energy of 1847 down to a paper on Clerk Maxwell's 
Theory of the Movements of the Ether, published 
in 1893, the year before his death, a succession of 
about thirty communications, mostly all of the first 
importance. So early as 1851 he measured the 
duration of induced electrical currents. 

For many years the conception of the action of 
Newton's law of gravitation dominated the minds of 
physicists, and suggested the notion of * action at a 
distance.' That is to say, it was supposed to be possible 
that one body might act upon another without the exist- 
ence of any tangible or intangible intervening medium. 
And yet this was not the opinion of Newton himself, 
for, in his third letter to Bentley, he wrote : c That 


gravity should be innate, inherent, and essential to 
matter, so that one body may act upon another at a 
distance, through a vacuum, without the mediation 
of anything else, by and through which their action 
and force may be conveyed from one to another, is to 
me so great an absurdity, that I believe no man, who 
has in philosophical matters a competent faculty of 
thinking, can ever fall into it.' 

The notion of action at a distance was the first 
conception of electrical action, and it found expression 
especially in the well-known law of Wilhelm Weber. 
He endeavoured to explain electrical attractions by 
the assumption of a force acting in straight lines, and 
following the same laws as the laws of gravitation. 
This was supported by Coulomb. Suppose two 
electrified bodies near each other, then the intensity 
of the force is inversely proportional to the square of 
the distance between the two quantities of electricity 
on their respective surfaces and directly proportional 
to the product of the two quantities. There is also 
repulsion between like, and attraction between unlike, 
electrical states. Further, it was supposed that this 
force was instantaneously propagated through space. 
Weber differed from Coulomb, in holding that both 
the velocity at which the electric quantities approached 
or separated, and also the acceleration of the velocity, 
had an influence on the amount of force exercised 
between the two bodies. Other similar hypotheses 
were in vogue, such as those of F. E. Neumann, 


his son, C. Neumann, Riemann, Grassmann, and 
Clausius. According to Helmholtz, the field of 
electrodynamics was at this time a pathless desert. 
( l So war das Gebiet der Elektrodynamik um jene 
Zeit zu einer unwegsamen Wiiste geworden.') l 
The theory of electrical action at a distance gave 
little satisfaction. 

Then arose the conception that actions between 
electrified bodies occupied time and required an in- 
tervening medium. The turning-point between the 
old and the new conceptions was reached in 1837, 
when Faraday published his experiments on the 
specific inductive capacity of substances. Faraday 
proved that the force of repulsion between two similar 
quantities of electricity depends not only on the 
quantities and on their distance apart, but also on the 
intervening medium. 2 The English philosopher had 
a genius for experiment, and he was guided by a 
marvellous insight into hidden processes. As has 
been well said by Clerk Maxwell, * Faraday, in his 
mind's eye, saw lines of force traversing all space, 
where the mathematicians saw centres of force 
attracting at a distance ; Faraday saw a medium 
where they saw nothing but distance ; Faraday sought 
the seat of the phenomena in real actions going on 
in the medium, they were satisfied that they had 

1 Introduction by Helmholtz to Die Prinxipien der Mechanik, von 
Heinrich Hertz, s. xi. 

2 An excellent account of electrical units is given by Magnus Maclean 
in his work on Physical Units. London, 1896. 



found it in a power of action at a distance impressed 
on the electric fluid.' Lord Kelvin writes, ' Faraday, 
without mathematics, divined the result of mathe- 
matical investigation ; and what has proved of infinite 
value to the mathematicians themselves, he has given 
them an articulate language in which to express 
their results. Indeed, the whole language of the 
magnetic field and lines of force are Faraday's. It must 
be said for the mathematicians that they greedily 
accepted it, and have ever since been most zealous in 
using it to the best advantage.' 

It was one of Helmholtz's mental qualities, that 
he was never satisfied with an inadequate explanation. 
He examined all the theories of electrical action 
and found them insufficient. His studies were at 
first of a critical nature, without experimental investi- 
gation. He showed that certain consequences of 
Weber's law were inconsistent with, or even contra- 
dicted, the law of the conservation of energy, although, 
on the other hand, they gave a satisfactory explana- 
tion of many of the facts. Helmholtz demonstrated 
that the law led to the idea of infinite speed, and 
also implied that the centre of gravity of static 
electricity was changeable. With Coulomb's state- 
ment, that electric forces act through space similar to 
gravitation, and follow substantially the same law, he 
was more in accord. He accepted Neumann's notion 
or law of potential with reservations. 

The special work of Helmholtz on electrodynamics 


has been thus shortly stated by Professor Riicker : l 
'From 1870 onwards, Helmholtz published an im- 
portant series of papers on the theory of electro- 
dynamics. His point of departure was the discussion 
of the mutual action of two current elements. An 
expression for the potential of two such elements had 
been formulated by F. E. Neumann, which differed 
from those deduced from the theories of W. Weber 
and Clerk Maxwell respectively. All three gave 
identical results in the case of closed circuits. Tak- 
ing the elder Neumann's formula as the groundwork 
of his investigations, Helmholtz sought to find the 
terms which must be added to it, so as to produce 
the most general expression consistent with the 
known behaviour of closed circuits. The result was 
an expression consisting of the sum of two terms, 
which were multiplied respectively by i + k and 
i - k, where k is an undetermined constant. The 
expression is equivalent to that given by Weber 
when k = - i, to that given by F. E. Neumann 
when k = i, and is in accord with Maxwell's theory 
when k = o. It was then proved that if k is 
negative the equilibrium of electricity at best must 
be unstable, so that motion, when once established, 
would increase of its own accord, and lead to infinite 
velocities and densities. The assumption was, in fact, 
a violation of the law of the conservation of energy 

1 Riicker, Obituary Notice of Helmholtz, Proc. Roy. Sec., vol. lix., No. 


in the sense that two electrified particles starting 
with a finite velocity would, within a finite dis- 
tance, acquire infinite speed, and therefore infinite 
energy. ... It remains, however, to discuss the 
case where k was equal to or greater than zero. 
The most interesting part of this investigation was 
the application of the generalised formula to the 
propagation of electrical and magnetic disturbances 
through bodies capable of electrical or magnetic 
polarisation. These properties were treated inde- 
pendently. . . . Both longitudinal and transversal 
electric disturbances can be propagated in unmagnet- 
isable dielectrics. The velocity of the transversal 
undulations in air depends on the absolute suscepti- 
bility of the medium. If this is very large the 
velocity is the same as that of light. The velocity 
of the longitudinal waves is equal to that of the 
transversal waves multiplied by the factor ij Jk, and 
by a constant which depends on the magnetic con- 
stitution of the air. In conductors the waves are 
rapidly damped. If the insulator is magnetisable, the 
magnetic longitudinal oscillations have an infinite 
velocity, the transversal magnetic oscillations are per- 
pendicular to the transversal electrical oscillations, 
and are propagated with the same velocity. In the 
particular cases when k = o the longitudinal waves 
of electricity have also an infinite velocity, and the 
theory is then in close accord with that of Maxwell, 
provided that the absolute specific inductive capacity 


of the air is great enough to make the common 
velocity of the electrical and magnetic transversal 
undulations equal to that of light.' 

Finding the notion of action at a distance in- 
consistent with dynamic principles and with ex- 
periment, he abandoned it and accepted Faraday's 
principle. Then followed, as the years went by, 
papers on the origin of electric currents and on 
their action in circuit, on galvanic polarisation 
of fluids free from gas, on the electrolysis of 
water, on galvanic currents due to differences of 
concentration of fluids, on electric border-plates, on 
currents on polarised platinum, on the galvanic 
polarisation of mercury, and on the capillary electro- 
meter. In some of these papers the method followed 
is less mathematical and more that of experiment 
and induction ; but in all the fundamental principle 
is the conservation of energy. In the tract on the 
conservation of energy he had shown long before that 
if the phenomena of Oersted and Ampere be assumed, 
that is, if a wire carrying an electric current is 
impelled across the lines of magnetic force, then the 
phenomenon discovered by Faraday follows necessarily, 
namely, a conductor moved across the lines of 
magnetic force shows an electromotive force whose 
intensity can be determined by the application of 
the equation of energy. 1 

Ampere had stated the laws of action between 

1 Tait, op. <:;.-., p. 89. 


conductors carrying currents, and he showed that 
the action of a small closed current at a distance is 
the same as that of a small magnet placed in the 
centre of the closed circuit, provided that the axis 
of the magnet is at right angles to the plane of 
the closed circuit, and that its magnetic moment is 
equal to the product of the area of the closed 
circuit into the current. This subject was extended 
mathematically by Helmholtz. 

Helmholtz introduced a new method of research 
into electrical questions by bringing in the idea of 
convection in the distribution of electricity, that is, 
the conveyance of electricity from one point to another 
by the movement of the material elements carrying it. 
It was important to determine whether or not the 
magnetic effects of an electric current were identical 
with those produced by the displacement of matter 
carrying an electrostatic charge. The experimental 
research on this subject was carried out in Helmholtz's 
laboratory by the well-known American physicist, 
H. A. Rowland, and the results were published in 
1876. Electrical convection currents throw some 
light on the movement of electricity in unclosed 
conductors ; while in electrolysis the gases dissolved 
in the fluid may also carry charges of electricity by 
convection. It was proved that a revolving charged 
conductor behaves like a ring-shaped electric current. 

With another American electrician, E. Root, 
Helmholtz, also in 1876, examined the polarisation 


effects of the occlusion of hydrogen on thin plates 
of palladium and platinum. They found that if a 
stream of hydrogen is directed to one side of a 
thin platinum plate by electrolysis, its presence is 
soon felt on the other side of the plate by the plate 
becoming more positive, and they showed that what 
was required by theory was fulfilled by experiment. 

In these investigations Helmholtz. made many 
subsidiary discoveries. Lord Kelvin and he inde- 
pendently established the reciprocal property of the 
electric charge of one conductor on another. Thus 
the potential of a body A due to a unit charge 
on B is equal to the potential of B due to a unit 
charge on A. He also invented a double galvano- 
meter, which was a modification of that of Gaugain. 
In the instrument of the latter the magnet was 
suspended, not at the centre of the coil, but at a 
point on the axis at a distance from the centre equal 
to half the radius of the coil. Helmholtz greatly 
improved the instrument, and made it more trust- 
worthy by placing a second coil, equal to the first, 
at an equal distance on the other side of the magnet. 1 
He also constructed an electro-dynamic balance not 
affected by the magnetism of the earth. 

On April 5, 1881, Helmholtz delivered the 
Faraday lecture to the Chemical Society On the 
Modern Development of Faraday s Conception of Elec- 
tricity^ in which he gave an interesting estimate of 

1 Jamin et Bouty, Cours de Physique^ t. iv. 2, p. 133. Paris, 1883. 


the great English physicist. 1 His words in opening 
the lecture are so characteristic of Helmholtz him- 
self as to merit quotation : c The facts which he 
[Faraday] discovered are universally known. Every 
physicist, at present, is acquainted with the rotation 
of the plane of polarisation of light by magnetism, 
with dielectric tension and diamagnetism, and with 
the measurement of the intensity of galvanic currents 
by the voltameter, while induced currents act on 
the telephone, are applied to paralysed muscles, and 
nourish the electric light. Nevertheless, the funda- 
mental conceptions by which Faraday was led to 
these much admired discoveries have not received 
an equal amount of consideration. They were very 
divergent from the trodden path of scientific theory, 
and appeared rather startling to his contemporaries. 
His principal aim was to express in his new con- 
ceptions only facts, with the least possible use of 
hypothetical substances and forces. This was really 
an advance on general scentific method, destined to 
purify science from the last remnants of metaphysics. 
Faraday was not the first, and not the only man, 
who has worked in this direction, but perhaps no- 
body else at his time did it so radically. But every 
reform of fundamental and leading principles intro- 
duces new kinds of abstract notions, the sense of 
which the reader does not catch in the first instance. 
Under such circumstances, it is often less difficult 

1 Trans, of the Chemical Society^ p. 277. 


for a man of original thought to discover new truth 
than to discover why other people do not understand 
and do not follow him. This difficulty must increase 
in Faraday's case, because he had not gone through 
the same common course of scientific education as 
the majority of his readers. Now that the mathe- 
matical interpretation of Faraday's conceptions re- 
garding the nature of electric and magnetic forces has 
been given by Clerk Maxwell, we see how great a 
degree of exactness and precision was really hidden 
behind the words, which, to Faraday's contemporaries, 
appeared either vague or obscure ; and it is in the 
highest degree astonishing to see what a large number 
of general theorems, the methodical deduction of 
which requires the highest powers of mathematical 
analysis, he found by a kind of intuition, with the 
security of instinct, without the help of a single 
mathematical formula. I have no intention of blam- 
ing his contemporaries, for I confess that many times 
I have myself sat hopelessly looking upon some 
paragraph of Faraday's description of lines of Force, 
or of the galvanic current being an axis of power, 
etc. A single remarkable discovery may, of course, 
be the result of a happy accident, and may not 
indicate the possession of any special gift on the 
part of the discoverer ; but it is against all rules of 
probability, that the train of thought which has led 
to such a series of surprising and unexpected dis- 
coveries, as were those of Faraday, should be with- 


out a firm, although perhaps hidden, basis of truth. 
We must also in his case acquiesce in the fact, that the 
greatest benefactors of mankind usually do not obtain 
a full reward during their lifetime, and that new ideas 
need the more time for gaining general assent the 
more really original they are, and the more power they 
have to change the broad path of human knowledge.' 

The lecture, however, was not merely a panegyric 
of Faraday. Helmholtz unfolded to the English 
chemists the theory of electrolysis, in its most 
modern form, as moulded by the law of the con- 
servation of energy, and the laws of electrolysis 
discovered by Faraday himself. Electricity can pass 
from the fluid to the electrodes only under condi- 
tions of equivalent chemical decomposition, which is 
brought about by the electrical forces splitting up 
the chemical compounds present. Helmholtz proved 
by calculation that the electric forces are quite 
sufficient for this work, as shown by the unexpected 
magnitude of the electrical equivalents that change 
places during the process. 

As already stated, p. 206, Helmholtz found that all 
the hypotheses of electrical action, such as those of 
Weber, the Neumanns, Riemann and others, ex- 
plained certain of the facts. For example, he found 
that they all accounted for the phenomena of elec- 
trical currents in closed circuits, but they did not 
do so for conductors which end in insulating non- 
conductors, or what might be called open or 


unclosed conductors. He was also of opinion that 
Wilhelm Weber's supposition that electrical quantities 
had inertia, like ponderable bodies, was highly improb- 
able. In 1879, Helmholtz set as a prize research 
for his students this question of the inertia of 
electricity, and, in 1880, it was won by Heinrich 
Hertz, who showed that if it has inertia at all, the 
latter could only have an influence of the smallest 
degree conceivable. This was the beginning of the 
famous work of Hertz, which resulted in the ex- 
perimental demonstration of Maxwell's magneto- 
electric waves, and has led to the invention of 
wireless telegraphy. 

The subject of electrical oscillations was investi- 
gated by Helmholtz in 1869 and 1871. In 1869 
he caused his pendulum myograph to close two 
circuits at short but measurable intervals of time. 
Oscillations were thus produced in a secondary 
circuit, the terminals of which were led off to a 
Leyden jar. The secondary circuit was then broken, 
and the electrical oscillation was transmitted to the 
sciatic nerve of a frog-muscle preparation. The 
number of twitches could thus be recorded. As the 
time between the completing of the primary and the 
breaking of the secondary current was increased in 
successive experiments, alternations in the violence 
of the twitchings of the muscle were noticed, and 
in all forty-five minima were observed. 1 In 1871, 

1 Riicker, op. cit., p. 27. 


Helmholtz, by his pendulum methods, determined 
the velocity of the propagation of electro-magnetic 
induction at 314,400 metres per second. 

Faraday had shown that the passage of electrical 
action involved time ; but, what was of even greater 
importance, he also demonstrated that electrical 
phenomena are brought about by changes in in- 
tervening non-conductors, or dielectric substances. 
The seat of electrical action was to be sought in the 
tensions and strains that occur in the dielectric 
medium. Upon this basis Clerk Maxwell founded his 
theory of electrodynamics. This theory, carried out 
to its logical conclusion, required that any electric 
disturbance should be propagated through what had 
been till then called the 'luminiferous' ether. 
Suppose a current passing in a metallic conductor in 
which there is a minute break or gap filled up by a 
non-conductor, such as air, the current, if sufficiently 
strong, will pass across the gap as a spark. If 
this action cause a disturbance in the dielectric, 
this disturbance should be propagated into space by 
the ether ? An imperfect analogy may help the 
mind at this point. What occurs at the gap 
may be like the effect of a stone dropped into still 
water, when a wave will be started and propagated 
from the centre of disturbance. Another disturbance 
will cause another wave, another a third wave, and 
so on. The shorter the interval of time between 
successive disturbances the shorter will be the waves. 


Is there anything analogous in magneto-electric 
action ? Fitzgerald was the first to suggest an 
attempt to measure the length of electric waves ; 
and Helmholtz propounded the question for a prize 
essay to be awarded by the Berlin Academy. 

It was reserved for Hertz, the favourite pupil of 
Helmholtz, to prove the correctness of Clerk 
Maxwell's theory, and actually to demonstrate the 
existence of electro-magnetic waves, or, as they are 
usually called, the Hertzian Waves. How he 
was led step by step to this great discovery, over- 
coming difficulties as they arose, and going into this 
unknown land in the firm belief that scientific theory 
would not lead him astray, has been fully described 
by Hertz himself. 1 He showed that waves of electric 
energy consist of displacements transverse to the direc- 
tion of transmission, and are governed by the same 
laws of reflection, refraction, and polarisation as those 
of light. Their velocity of transmission is the same as 
that of light, 300,000 kilometres per second (186,380 
miles per second, in vacuo ; Michelson, 1879). As 
the electric oscillations produced by the Hertzian 
method are comparatively few in number per second, 
when the velocity of light is divided by this number, 
the resultant wave-length is still found to be im- 

1 Hertz. Electric Waves. Trans, by Jones, with preface by Lord 
Kelvin. London, 1893. See especially the Introduction, p. I. See also 
a lecture by Hertz On the Relations between Light and Electricity, delivered 
on Sept. 20, 1889, and printed in his Miscellaneous Papers, trans, by 
Jones, p. 313. London, 1896. 

2I 7 


mensely greater than that of light, varying from 
decimetres to kilometres, while the waves that fall on 
the retina, and constitute what we call light, have a 
wave-length of only from 0-3 to 07 thousandths of a 
millimetre. 1 Then, by the principle of 'resonance,' 
(using this word in a special sense), the waves may 
be detected as minute sparks, or by acting on an 
arrangement called a coherer. 2 Hence wireless tele- 
graphy ! 

Hertz always referred the inspiration to Helmholtz, 
and W. von Bezold gives his impression of the 
memorable occasion when Helmholtz reported to the 
Academy on the researches of his distinguished pupil. 
'The impression will never be forgotten by any- 
one. . . . The most intense and purest joy shone in 
the countenance of the great master, who explained in 
eloquent words, and with the freshness of youth, the 
importance and influence of this fundamental work.' 
This was in 1888. Six years later, on the ist of 
January 1894, Hertz died before the completion of 
his thirty-seventh year. Helmholtz wrote of him 
these words : ' The news of the death of this 
favourite of genius was a severe shock to all who 

1 Relation between British and metric units of length and mass : 
i yard = o'9i439i79 metre; i metres 1-09362311 yards = 39-370432 
inches ; i pound = 0-453593 kilogramme ; i kilogramme = 2-20462 12 
pounds; also, i kilometres 1000 metres; i millimetre j^njth 
metre = ^th inch. 

2 Kerr. fTireleti Telegraphy. London, 1898. Also, Andrew Gray's 
Treatise on Electricity and Magnetism, vol. i.. London, 1898, chap, xi., 
for a full description of the Hertzian Vibrator and Receiver. 



recognise the development of the individual, both as 
regards mental capacity and the victory of the soul 
over the passions and opposing powers of nature. 
Endowed with the rarest gifts of mind and character, 
he has in his short life reaped a harvest in a field in 
which many of the most talented of his scientific 
brethren had laboured in vain. In classical times his 
death would have been regarded as a sacrifice to the 
envy of the gods. Nature and fate co-operated in his 
development. In him we found all the qualities 
required for the solution of the hardest problems in 
science. . . . Heinrich Hertz appeared to be pre- 
destined to disclose new vistas into the unpenetrated 
depths of nature ; but all these hopes were crushed by 
the insidious disease which slowly and unceasingly 
crept on until it destroyed the life we esteemed so 
valuable. I myself deeply felt the loss, as I have 
always looked on Hertz as the one of all my students 
who had entered into the innermost circle of my 
scientific thoughts, and the one in whose ultimate 
development and success I dared to place my surest 
hopes.' In a few months the great master followed 
his pupil to the grave. 

Among the last papers written by Helmholtz was 
one on Clerk Maxwell's theory of the movements in 
the free ether, in which he discussed profound ques- 
tions as to whether it were free to. move, to what 
extent and how it was associated with gross matter, 
and he shows that its incompressibility being assumed, 


all its changes and movements can be deduced from 
the laws of electrodynamics, and the principle of 
least action. 

4. On Meteorological Physics. 

Like all brain workers, Helmholtz found it 
necessary to spend part of the year, mostly during 
the interval between the summer and winter sessions 
of academic work, in the country, and he was in the 
habit of going to the Alps, to the south of France, 
and occasionally to England. One can readily under- 
stand that a mind like his was always receptive, and 
that the sights and sounds of nature in the magni- 
ficent aspect of mountain and valley, in the green 
woodland and on the rocky coast by the sea, were a 
source of the purest enjoyment. But the intellect 
never slumbered. Accordingly, we find that he 
endeavoured, now and again, to explain natural 
phenomena, such as the formation of clouds, the 
mechanical conditions of the whirlpool or whirlwind, 
and the formation of glaciers. It would be wrong to 
suppose that this habit of the scientific analysis of 
one's impressions of natural effects diminishes the 
aesthetic enjoyment ; we should rather conclude that 
aesthetic enjoyment may be of different kinds. The 
poet simply opens his mind to nature, receiving all 
her impressions, he has his imagination fired, and his 
heart touched by the feelings of beauty, while he 



yearns to give expression to his feelings in adequate 
form. To him, possibly, an analysis of how these 
effects are produced might destroy the charm, and 
might even lead him to give a wrong interpretation 
of what was before his eyes, as was the case when 
Goethe attempted to explain colour by an utterly 
erroneous conception. But the man of science, who 
has in him a love of nature, and an imagination akin 
to that of the poet, and often more penetrating, must 
strive towards the intellectual satisfaction of under- 
standing the methods by which nature works. 

In one of his papers on hydrodynamics, Helmholtz 
refers shortly to the theory of tidal action. The 
tendency of tidal movements on the surface of a planet 
is to retard its rotation till at last it turns always the 
same face to the body that causes the tidal motion. 
Helmholtz was the first to point out that the reason 
why satellites generally turn the same face to their 
primary, is to be found in the tides produced by the 
primary on the satellite while it was yet in the molten 
state. 1 

The movements of glaciers and the formation of 
ice arrested his attention, and it so happened that at 
that time the observations of Rendu, Forbes and 
Tyndall were being discussed. Helmholtz's contribu- 
tions to the ice theory were published in 1865 and 1866, 
while he was in Heidelberg. Faraday had made the 
familiar observation that two pieces of ice pressed against 

1 Tait, Thermo-Dynamics, p. 104. 


each other at zero (centigrade) freeze into one block. 
James Thomson, the brother of Lord Kelvin, had 
explained this by showing that pressure causes a 
lowering of the freezing point. James Thomson de- 
duced this fact from the mechanical theory of heat. 
Lord Kelvin soon after gave the complete theory 
connecting melting point and pressure, and verified 
by experiment his brother's calculation that each in- 
crease of a pressure of one atmosphere causes a 
lowering of the freezing point to T ^-g of a degree 
cent. A mixture of snow and ice becomes colder 
as pressure increases, just as theory requires. In 
Faraday's experiment mentioned above, some free 
heat becomes latent during pressure, a part of the ice 
along the side of the block melts and then freezes 
again, cementing the blocks into one piece. These 
facts, and also the remarkable phenomenon of the 
well-known movements of a hard, and, in popular 
belief, a brittle body, like ice in great glaciers, 
were originally accounted for by regarding ice as a 
viscous fluid, a suggestion due to Rendu, a Savoyard 
priest, and very fully developed by the celebrated 
natural philosopher, James Forbes. Helmholtz, by 
a large number of experiments, in which ice was 
submitted to varying degrees of pressure, succeeded 
in imitating the formation of glacial ice. Lord 
Kelvin also showed that cobbler's wax behaved like 
a viscous fluid. In the course of months or years, 
it will gradually flow down an inclined plane as a 



glacier flows down a valley, showing the curves and 
stream lines as in the true glacier. It is a curious 
sight to watch corks, if left to themselves for a 
long time on the surface of the wax, ultimately 
float on it, just as bodies left on the surface of a 
glacier may by-and-by be found deeply embedded in 
the apparently brittle substance. 

In one of his lectures Helmholtz gives an explana- 
tion of waterspouts. He shows that the whirling 
water forms a vertical tube full of air. Probably his 
most interesting contribution to meteorological physics 
is contained in two papers on the movements of the 
air published in 1888 and 1889. This was followed 
by one in 1890 on the Energy of Winds and Waves. 1 
In these he develops the mathematical theory of the 
formation of cloud strata. It is said that in one of 
his Alpine excursions he saw, from the summit of the 
Rigi, the grand spectacle of a table-land of clouds 
below him, and the appearance suggested that of 
waves on the sea seen from the height of a rocky 
coast. The formation of cloud waves was suggested 
from the formation of water waves, the fundamental 
idea being that a plane surface of water over which a 
wind of uniform velocity is blowing is in a state of 
unstable equilibrium, and that waves thus originate. 
Here we have two fluids, air and water, of different 
densities, gliding over each other. While friction in the 
upper regions of the air must be very slight, it will 

1 Wissenschaftl. Abhandlungen, Bd. iii., 8. 289 ; 8. 309 5 s. 333. 
22 3 


be found at surfaces of separation between two layers 
and along the borders of rotating masses. 

Helmholtz drew special attention to the manner 
in which, according to the kinetic theory of gases, 
viscosity and interchange of temperature take place 
across such surfaces of separation. We may suppose 
that in the upper regions of the atmosphere there 
are contiguous layers of air of different densities, 
temperatures and velocities. If no watery vapour 
condenses at the surfaces across which interming- 
ling takes place nothing will be seen. But should 
there be condensation of vapour, clouds will be 
formed ; and then, just as wind raises waves on 
the surface of the ocean, so cloud waves will be 
formed on the side of the less dense layer. The 
action will not take place in a quiet steady manner, 
but by fits and starts, being, indeed, a case of dis- 
turbed equilibrium. The effect is well seen in the 
beautiful wavy appearance of barred cirrhi clouds, in 
which the shining white bars correspond to the wave- 
troughs, and the thin translucent bars, through which 
the light of the blue sky penetrates, to the wave crests. 
Helmholtz, at Cap d'Antibes, measured the velocity 
of the wind with an anemometer, and counted the 
number of waves on a given surface of sea, and thus 
obtained data on which to base his calculations. He 
thus found the connection between the strength of the 
wind and the length of the waves. The water waves 
were compared as to length with cloud waves. A 


moderate wind blowing over the surface of water 
will give rise to waves of about a metre in length (a 
little more than a yard) ; the same waves, in cloudland, 
at the border of two layers of air, differing in tempera- 
ture by 10 C. will have a length of two to five kilo- 
metres (about 2-| miles). Sea waves may reach a 
length of five to ten metres (say 12 yards), and 
as these would correspond to cloud waves of from 
fifteen to twenty kilometres (say over 10 miles), we 
can grasp the notion that one of these long cloud 
waves may, at a particular time, cover all the sky 
above our head. That these views of Helmholtz on 
cloud formation are correct, has been supported by 
many observations since made in balloon voyages. 
It has always been found that in traversing regions 
in which there are great plains of cirrhi clouds, a 
sudden change of temperature is noticed in passing 
from one layer of air into the other. 

5. On Physical Optics. 

A slight sketch has already been given in Chapter 
VIII. of Helmholtz's researches in physiological optics, 
and the whole is narrated in full detail in a new edition 
of his great work, Handbuch der physiokgtschen Optik^ 
published in 1894, the year of his death. In this 
work the dioptrics of the eye are fully discussed, with 
a wealth of illustration and mathematical power that 
is truly astonishing. The laws of refraction from 


spherical surfaces, the properties of cardinal points, 
and the theorems of Gauss relative to the refractive 
powers of centred systems of spherical surfaces, all 
matters relating to what may well be called physical 
optics, are discussed, so that, in forming an estimate 
of all that Helmholtz has accomplished in this depart- 
ment of science, the treatment of these subjects in a 
work mainly physiological must not be forgotten. 
Nine papers, however, are enumerated in his collected 
works as specially belonging to physical optics. Five 
of these relate to colour, and might well have been 
included in the list of fifteen works on physiological 
optics, so that only four remain. One of these, 
published in 1867, is a mathematical essay dealing 
mainly with the action of lenses; two, issued in 1873 
and 1874, deal with the higher optical principles of 
the compound microscope and the limits of magnifica- 
tion ; and the last, which was also issued in 1874, 
relates to the theory of anomalous dispersion. Finally, 
in 1892, there appeared a paper, important from a 
theoretical point of view, in which he applied Clerk 
Maxwell's electro-magnetic theory of light to explain 
the dispersion of colour. 1 

In this connection, and as it is a matter of practical 
interest, it may be pointed out that Helmholtz was 
often in the habit of magnifying small movements 
by reflecting a beam of light from a small mirror 

1 All the papers on light appear in Bd. ii. Whsenschaftl. Abhandlungen ; 
that on colour dispersion in Bd. Hi., s. 505. 


attached to a suitable part of the apparatus that 
was in motion. But he was not the inventor of 
this method, as has sometimes been erroneously 
stated. Poggendorff, in Vol. VII. of his Annalen^ 
issued in 1826, describes an experiment in which he 
attached a mirror to a magnetised bar, and from 
this mirror a beam of light was reflected into a 
theodolite. This was the first example of making a 
beam of light act as a weightless pointer, and thus to 
amplify and indicate movement upon a scale. The 
method has been of the greatest service to physical 
science, and is seen to perfection in the arrangements 
of Lord Kelvin's electrometer and galvanometer. 

Newton established that white light consists of 
innumerable different homogeneous constituents which 
are dispersed by refraction. This is proved by passing 
white light through a prism, when a spectrum is pro- 
duced. The index of refraction becomes greater and 
greater as we pass through red to orange, orange to 
yellow, yellow to green, green to blue, blue to indigo, 
and indigo to violet, the violet rays being often described 
as the most refrangible of visible rays. It is also 
known that if certain media are placed in the path of 
the beam of light, and the light is then passed through 
a prism, certain parts of the spectrum show dark bands, 
known as absorption bands. This is well seen when 
a layer of blood sufficiently diluted is examined with 
a spectroscope. Two absorption bands may then 
be detected, one next the Frauenhofer line D, 


narrower than the other and blacker, while the 
broader band is more towards the right, that is, nearer 
E. The remaining part of the spectrum shows all 
the colours with beautiful clearness. The analysis of 
light by means of the spectroscope affords, then, a 
ready means of examining the phenomena of absorp- 
tion, an example of which has already been given in 
treating of Helmholtz's explanation of the fact that 
the mixture of a yellow with a blue pigment produces 

The peculiar phenomenon of anomalous disper- 
sion is closely associated with that of absorption. 
It was first discovered by Fox Talbot about 1870.* 
The experiment of Fox Talbot was as follows : c I 
prepared some square pieces of window glass, about an 
inch square. Taking one of these, I placed upon it a 
drop of a strong solution of some salt of chromium, 
which, if I remember rightly, was the double oxalate 
of chromium and potash, but it may have been that 
substance more or less modified. By placing a second 
square of glass on the first, the drop was spread out in 
a thin film, but it was prevented from becoming too 
thin by four pellets of wax placed at the corners of 
the square, which likewise served to hold the two 
pieces of glass together. The glasses were then laid 
aside for some hours until crystals were formed in the 
liquid. These were necessarily thin, since their thick- 

1 Proc. Roy. Soc. Edin., 1 870-71. See also Tait on Light, p. 156. 
Edinburgh, 1884. 



ness was limited by the interval between the glasses. 
Of course the central part of each crystal, except the 
smallest ones, was bounded by parallel planes, but the 
edges were bevilled at various angles, forming so many 
little prisms, the smallest of them floating in the liquid. 
When a distant candle was viewed through these 
glasses, having the little prisms interposed, a great 
number of spectra became visible, caused by the in- 
clined edges. Most of these were no doubt very 
imperfect, but by trying the glass at various points, 
some very distinct spectra were met with, and these 
could, with some trouble, be isolated by covering the 
glass with a card pierced with a pin-hole. It was 
then seen that each prism (or oblique edge of the 
crystal) produced two spectra oppositely polarised and 
widely separated. One of these spectra was normal ; 
there was nothing particular about it. The colours of 
the other were very anomalous, and, after many experi- 
ments, I came to the conclusion that they could only 
be explained by the supposition that the spectrum, 
after proceeding for a certain distance, stopped short and 
returned upon itself. 1 

The words italicised show that Fox Talbot dis- 
covered the real nature of this curious phenomenon. 
Le Roux, in 1860, had found that vapour of 
iodine, which allows only red and blue rays to pass, 
refracts the red more than the blue, the opposite of 
the effect of a glass prism. An alcoholic solution of 
fuchsine (an aniline colour) gives a dark absorption 


band in the green, and it was found that the refrac- 
tive index rises (as in normal bodies) for rays from 
the red to the yellow. But all the rest of the 
transmitted light, consisting of the more refrangible 
rays, is less refracted than the red. From some 
experiments of De Klecker, published in 1879, it 
would appear that ' The addition of fuchsine to alcohol 
alters the speed of propagation of the (so-called) less 
refrangible rays, but not perceptibly that of the more 
refrangible.' I 

The phenomenon had been examined by many 
physicists ; but the explanations were unsatisfactory. 
Helmholtz's first solution was founded on the sup- 
position that in transparent media certain ponderable 
molecules participate in the vibrations of the ether 
surrounding them. Mathematical difficulties arise if 
we suppose that there is discontinuity between the 
surfaces of these particles and that of the ether 
everywhere in contact with them, so he further 
assumes that there is continuity, that is, that 
there is no abrupt transition. Now, imagine light 
falling on such an arrangement. Part of the vibra- 
tions transmitted by the ponderable molecules is 
transformed into irregular vibrations, that is to say, 
into heat. Thus part of the light is absorbed or 
disappears. The ponderable medium opposes to the 
movement of the vibrating molecules a resistance like 

1 Tail, Light, p. 157. See also Jamin et Bouty, Cours de Physique, t. 
iii., p. 542. 



that of friction. Each molecule of the ether is thus 
affected by ( i ) an elastic reaction of the ether ; 
and (2) a force due to the ponderable medium, 
which is supposed to be proportional to the relative 
displacements of a molecule of ether and a molecule of 
ponderable matter. The ponderable molecule, on the 
other hand, is acted upon (i) by a force equal to, 
and in the reverse direction of, the preceding ; (2) a 
force due to the neighbouring ponderable molecules ; 
and (3) a retarding frictional force proportional to 
the rapidity of displacement. These conditions 
mathematically expressed lead to the differential equa- 
tions of motion. When there is no sensible absorp- 
tion, the formulae indicate a normal dispersion, but 
when great absorption takes place, theoretical results 
are obtained in accordance with those observed in 
anomalous dispersion. Thus, as expressed by Professor 
Tait, Helmholtz's explanation 'depends upon an 
assumption as to the nature of the mutual action 
between the luminiferous ether and the particles of 
the absorbing medium, coupled with a farther assump- 
tion connecting the absorption itself with a species of 
friction among the parts of each absorbing particle.' 
These assumptions were first suggested by Allenmeier, 
but they were fully applied by Helmholtz. 

This explanation was offered in 1874, but he re- 
turned to the subject in 1892 and 1893, and endeavoured 
to account for the fact in accordance with Clerk 
Maxwell's electro-magnetic theory of light, by the 


conception of pairs of oppositely charged particles 
(ions) of inert matter fixed in the ether. This paper 
probably contributed more to supporting the electro- 
magnetic theory of light than to an adequate ex- 
planation of anomalous dispersion, which is an easily 
demonstrable fact still incapable of explanation. 

It was in 1873 and 1874 that Helmholtz wrote two 
important papers on the Optical Principles of the 
Compound Microscope, and determined the limits of 
amplification. This was accomplished independently 
of similar and even more elaborate work, both mathe- 
matical and experimental carried out by the greatest 
living authority on all such questions, Professor Abbe of 
Jena, to whose researches, especially in connection with 
the construction on correct principles of apochromatic 
lenses, science owes so much. Helmholtz, in the first 
place, established a formula by which we can express 
the ratio of the linear magnitudes of the object and its 
image, in terms of the divergence of the rays before 
and after refraction, which is independent of the 
distance of the focal lengths of the refracting surface. 1 
He showed also how to measure and define the 
angle of aperture, and finally proved that in conse- 
quence of the dispersion of light at the edges of 
minute bodies, no objects can be seen that are smaller 
than the -^V^th of a millimetre, that is, the TT ^nriT th 
of an inch. So far the microscope can go and no farther. 

1 Heath's Geometrical Optics, p. 56. 

2 3 2 




6. On the Principles of Dynamics. 

T N his later years, Helmholtz was much occupied 
J- with the discussion of dynamical questions of 
the most abstruse nature. To him all physical 
phenomena were ultimately to be explained on 
dynamical principles, not merely those evident to 
the senses, but those in the greater world of mole- 
cular action. His mental vision penetrated below the 
surfaces of things, and to such a mind the mazy dances 
and whirls of atoms were ruled as rigidly by dynami- 
cal laws as were the movements of the planetary bodies. 
It was also characteristic of his mental capacities that 
they seemed to increase in power as time went on. 
In his old age he was not satisfied merely with the 
contemplation of what he had done, although that of 
itself must have been a source of supreme satisfaction, 
nor did he rest merely on his experience of men and 
things, but he was ever passing into higher regions of 
thought. Here he was engaged, not in the gathering 


of facts, but in the establishment of great principles, 
which would be applicable to abstract dynamics, 
hydrodynamics, thermodynamics, electrodynamics, 
alike, and by which insight might be obtained into 
hidden processes. In 1884 we find three elaborate 
mathematical papers on what he termed monocyclic 
systems; in 1886, a paper on the principle of least 
action ; in 1887, another on the same subject ; and in 
1892, a third paper on the principle of least action in 

Cyclic systems are those in which there are periodic 
or circulating motions. This is a somewhat vague 
description, but it may indicate what is meant. A 
motion definable by a single co-ordinate, like that 
of a circular disc spinning round its axis, he termed 
monocyclic, but he also conceived the more com- 
plicated case of a polycyclic system definable by 
a large number of co-ordinates, satisfying certain 
assumed conditions. The position of a disc in a 
monocyclic system depends on the angle which a 
plane containing the axis imakes with a plane fixed 
in space ; but the energy depends on the angular 
velocity. The potential energy remains unaltered 
while the disc revolves. The broad lines of the 
methods by which such systems may be investi- 
gated were first laid down by Thomson (Lord 
Kelvin) and Tait. Helmholtz narrowed the dis- 
cussion to certain types of such systems. He 
assumes for such that neither the kinetic nor the 


potential energy depend on the uncontrollable co- 
ordinates themselves (that is, co-ordinates incapable 
of being affected by the action of any external 
system), but only on the velocities corresponding 
to them. Further, he assumes that the velocities 
corresponding to the controllable co-ordinates are 
always very small in comparison with the others, 
and further, that the accelerations of the uncontrollable 
or cyclic velocities are also small. These assumptions 
imply that no forces depend on the cyclic co-ordinates. 
Changes in the cyclic velocities may change the energy 
of the system, but changes in the cyclic co-ordinates 
cannot do so. 1 Helmholtz also studied the effects of 
one monocyclic system on a neighbouring one, and of 
two or more monocyclic systems held together by a 
common band. The chief interest of these investiga- 
tions arises from the fact, that thermodynamic pheno- 
mena (more especially those related to the second law) 
show the peculiarities of monocyclic systems. One 
may also say that the value of the work of Helm- 
holtz in this department is, that his conceptions of 
monocyclic and polycyclic systems have such general 

Helmholtz showed that the principle of least action 
enunciated in 1744 by Maupertuis, and expanded by 
William Rowan Hamilton, the inventor of quaternions, 
is even a greater and more comprehensive generalisa- 

1 For a discussion of these difficult matters, see Gray, Treatite on 
Electricity and Magnetism, vol. i., chap. 7, p. 1 80. 


tion than that of the law of the conservation of energy. 
This law is not of itself sufficient to give a dynamical ex- 
planation of the mutual actions or relations of a system. 
The principle of least action, however, gives a dyna- 
mical process from which, with certain assumptions, 
those relations can be deduced. Maupertuis, who was 
a contemporary of Voltaire, and one of the brilliant 
group of men gathered around him by Frederick the 
Great, saw in his principle an indubitable proof of the 
existence of God, but he was not able to give it a 
mathematical form, nor could he have foreseen how 
important it was destined to become in general dyna- 
mics. For a long period it was only a metaphysical 
conception, even although mathematicians of the 
first rank endeavoured to express it in the language 
of dynamics. 

The subject has been fully treated, without the aid 
of formulae that are bewildering to the uninitiated, 
by Professor Leo Koenigsberger, in his admirable 
address on the Researches of Helmholtz in Mathe- 
matics and Mechanics, delivered in 1895, the year 
after the decease of Helmholtz. I 

Descartes founded analytical geometry, which, by 
determining the distances of all points by fixed lines, 
or co-ordinates, reduced spatial relations to their arith- 
metical expression, and by the use of algebraic 

1 Rede -zum Geburtsfeste des hochitseligen Grossher-zogi Karl Friedrtch 
und zur akademischen Preiivertheilung, am 22 Nov. 1895, von ^r keo 
Koenigsberger, Professor der Mathematik. Heidelberg, 1895. 
2 3 6 


equations solved geometrical problems, and demon- 
strated geometrical propositions. Descartes's error in 
theoretical physics was in conceiving matter as moved 
only by impulsion and pressure, and not by internal 
forces ; but he recognised that the quantity of matter 
and motion in the universe remained unchanged. He 
also defined the quantity of motion as being equal 
to the product of mass and speed (m v). The next 
great name in this arena of thought is Leibnitz, who, 
about the same time as Newton was engaged on 
establishing the differential calculus or calculus of 
fluxions. He argued that it was rather the quantity 
of vis that remained unchanged in the universe, and 
he defined this quantity as the product of the mass 
and the square of the speed (m v 2 }. The two views 
led to a schism among thinkers, some supporting 
Descartes, among those Euler, while others were on 
the side of Leibnitz. Kant admitted the Leibnitzian 
view with a limitation. It is, however, wholly, a 
question of definition and of nomenclature. If we 
mean by a force, a cause proportionate to the quantity 
of motion of a body, the Cartesian principle applies ; 
but if we mean by force, the power of a body to 
overcome a continuous and uniform resistance, the 
formula of Leibnitz holds good, namely, that the 
work performed by the force is equal to the pro- 
duct of half the mass into the difference of the 
squares of the speeds at the commencement and at 
the end of the motion. Both principles were recog- 


nised by Newton ; and in the language of the present 
day m v (mass into speed) is the quantity of motion 
or momentum, and m v 2 (mass into square of speed) 
is twice the kinetic energy. 

From a consideration of the principles of the lever, 
the pulley and the inclined plane, came the definition 
of work as the product of the quantity of a force into 
the minute movement of a material point measured in 
the direction of the force. This led to the establish- 
ment of the principle of virtual velocities according 
to which any material system is in equilibrium only 
when for every virtual or infinitely small movement 
compatible with the connections of the points, the 
work of the entire system is equal to zero. From 
Galileo's doctrine of inertia, and the enunciation of 
Newton's three laws of motion, a basis was formed for 
theoretical dynamics. The more important of these 
laws in the present connection are the first and second. 
The first asserts that every body continues in a state 
of rest or of uniform motion in a straight line, unless 
compelled to change that state by the action of some 
external force ; in other words, it expresses the prin- 
ciple of inertia. Force may be defined as that which 
changes or tends to change the state of rest or motion 
of a body, and force is measured by the change of 
momentum it produces in a unit of time. In the idea 
of momentum, the quantity of matter moved (mass) 
is taken into account as well as the rate at which it 
travels. This leads to the second law. Rate of 


change of momentum is proportional to the impressed 
force, and takes place in the direction in which the 
force acts. Then we have the third law, that to 
every action there is always an equal and opposite 

Greater precision is introduced by adopting the 
Gaussian notion of unit force. If a unit of force 
act for a unit of time upon a unit of mass, the 
velocity of the mass will be changed, and the total 
acceleration will be unity in the direction of the 
force. Further, in accordance with Newton's Second 
Law, the magnitude and direction of this total 
acceleration will be the same whether the body is 
originally at rest or in motion. Again, when any 
number of forces act on a body, the acceleration 
due to each force is the same in direction and magni- 
tude as if the others had not been in action. 1 

It was about this stage that Huygens, Leibnitz, 
and the Bernoullis contributed to the discussion, 
but their arguments were often of a metaphysical 

Half the product of the mass of a particle into 
the square of its speed is its kinetic energy. A 
material system may have any number of such par- 
ticles, and the sum of the individual kinetic energies 
will become the kinetic energy of the system. 
Further, any increase in the kinetic energy of a 
material system in passing from one configuration 

1 Clerk Maxwell, Matter and Motion, p. 42. London, 1876. 


into another is equal to the work done on the 
system by the external forces. If these forces 
depend upon positions and mutual distances of the 
particles, the system, after a change from one con- 
figuration into another, and a return to its original 
condition, will suffer no change in kinetic energy. 
Such a system is described as conservative. When 
a conservative system, in its change from one con- 
figuration into another, does a certain amount of 
work, then its power of doing work in virtue of 
its configuration, or, in other words, its potential 
energy, is greater in the first position than in the 

In this way we arrive at a statement of the law of 
the constancy of energy, which asserts that, in the 
motions of any conservative system, the sum of the 
potential and of the kinetic energy is unchangeable. 
This, of course, implies the impossibility of the per- 
petual motion, or the production of work from 
nothing, because if it (the perpetual motion) were 
possible, we might gain work by changing the 
system one way and then back again by a different 
route to its original condition. This principle of 
conservation was long recognised in a limited sense, 
but it did not seem to apply to all kinds of forces. 
Thus, if a system moves backwards and forwards 
on the same track, first without and afterwards with 
friction, then the friction in the latter case will 
diminish the velocity, and there will be a loss of 


kinetic energy. Consequently we must extend the 
conception of energy from that of potential energy, 
or the energy of position, so as to include the energy 
of motion, which may appear as heat or other forces. 
The loss of kinetic energy in the above case will then 
be equal to the amount of heat produced. This idea 
led Mayer (see p. 47) to the fundamental conception 
of the equivalence of heat and mechanical work, and 
it no doubt also guided Helmholtz in writing his tract, 
Die Erhaltung der Kraft. The outcome of this dis- 
cussion is that the work done by any conservative 
system in changing from one configuration into 
another, depends on the configurations at the be- 
ginning and the end of the process, and not on the 
intermediate stages. The tract was intended to show 
the theoretical and practical importance of the law 
of the constancy of energy, not from a priori con- 
siderations, but by induction from facts, and especially 
from vain attempts to discover or invent the per- 
petual motion. It does not tell us anything about 
the mode by which the configuration is changed, or, 
to put the matter in other words, it does not define 
the route followed by the system in passing from the 
first configuration into the last. 

The publication of this tract, which has had so 
great an influence on science, was often referred to 
in later years by Helmholtz. It was therefore fitting 
that he should crown the edifice he had reared by 
the great papers of his later years, in which he re- 


turned, with mature powers and with the enormous 
experience gained in many fields of physiological 
and physical research, to the problems of his early 
youth. As already explained, the notion of action 
at a distance was gradually but completely abandoned, 
and its place was taken by that of a medium 
connecting masses of matter with each other, and 
transmitting force. But if this new conception is 
still mechanical, if particles of matter are straining 
upon the invisible ties that bind them together, if 
all attractions and repulsions occur in the medium 
known as the ether, what is the simplest expression 
of the laws that control these dynamical operations ? 
Can any general principle be established by which, 
and even without experiment, these dynamical opera- 
tions can be deductively explained ? It was felt by 
many that, even with the help of Galileo's notion 
of inertia and Newton's laws, some mechanical con- 
ceptions, such as statical equilibrium, or the theory 
of virtual velocities, were not fully proved ; while, on 
the other hand, many phenomena, molecular, chemi- 
cal, electrical, magnetical, were hidden from direct 
observation and immediate experience. The enuncia- 
tion of the law of the conservation of energy changed 
the aspect of affairs, and gave a great impulse to the 
development of theoretical dynamics. The notion 
of force fell into the background, while mass and 
energy became recognised as indestructible quantities. 
Energy was twofold : kinetic energy depended in all 


cases on the speeds of the moving masses ; potential 
energy by the positions of the masses in any system. 
The discussion of the different modes of energy, and 
the conditions of the passage of one mode of energy 
into another, became the subject-matter of physics 
and chemistry. Helmholtz did not, as had hitherto 
been done, deduce the general principles of mechanics 
from equations of motion, but he started from a more 
general principle, that of least action. The papers on 
this subject are, according to Hertz, the high-water 
mark of modern physics. 

Action, according to Leibnitz, was the product of 
the mass, the distance through which it was moved, 
and the speed. In other words, the product of the 
vis viva (twice the kinetic energy), and the time. 
According to this view, when a body passed from 
one configuration into another, the total amount of 
the action had a limit value, while the amount of 
the energy remained unchanged. The element of 
time came into the statement, so that the position 
of individual parts of the system at specific times 
during the whole time occupied by the change of 
configuration could also be taken into account. 
Lagrange and Hamilton also introduced the idea, 
that, while the relative amount of potential and 
kinetic energy were constantly changing, the amount 
of this change must also be considered ; while 
Jacobi, assuming that the potential energy is inde- 
pendent of time, gave the kinetic energy a certain 


value, and thus eliminated the increment of time 
from the action. Hamilton stated the principle of 
least action in yet another form. 1 He showed that 
the complete solution of any kinetical problem, as 
regards the action of any conservative system of 
forces and constraint depending on the reaction of 
smooth surfaces or curves, is reducible to the deter- 
mination of a single quantity, which he called the 
characteristic function of the motion. This quantity 
is found from a partial differential equation of the 
first order and second degree, and from the com- 
plete integral of this equation all the circumstances 
of the motion may be deduced by differentiation. 
This has been called the method or principle of 
varying action. 2 

The principle of least action may be thus briefly 
stated : Given a conservative system in any con- 
figuration, and different paths by which it could be 
guided to any other definite configuration, under the 
condition that the sum of its potential and kinetic 
energies is constant, then the path for which the 
action is least is the one along which the system 
would move unguided if the proper initial velocities 
were given to it. The term action^ as applied to a 

1 W. R. Hamilton on a General Method of Dynamics. Phil. Trans. 
1834, 1835. 

2 Thomson and Tail's Natural Philosophy, vol. i., pt. insect. 333 ; also 
Tail on the Application of Hamilton 1 s Characteristic Function to Special Cases 
of Constraint. Trans. Roy. Soc. Edin^ vol. xxiv., and Scientific Papers, vol. 
i., p. 54. 



moving system for a short interval of time, is usually 
defined as the product of double the average kinetic 
energy during that time, multiplied by the time ; or, 
shortly, it is double the time-integral of the kinetic 
energy. Discussions based on this definition give the 
action in terms of the initial and final co-ordinates of 
the system and the time prescribed for the motion. 
Again, action may be expressed in another way, as 
the sum of the products of the average momentum 
for the spaces through which particles move, multi- 
plied by the length of the spaces. For double the 
kinetic energy during a short interval of time multi- 
plied by the time, is equal to the average momentum 
during that time multiplied by the space described. 
Investigations on the second definition of action 
give the action in terms of the initial and final 
co-ordinates of the system, and the constant sum 
of the potential and kinetic energies. 1 

It is not easy finding simple examples of the appli- 
cation of the principle ; nor can it be said that the 
fundamental dynamic significance of the principle has 
been made clear. Quantities like velocity, momentum, 
kinetic energy, potential energy, are what might be 
called instantaneous properties of a system. Their 
values are definite at each instant, and can be assigned 
without reference to what has taken place previously. 
But the Action of a system at any instant depends on 

1 Thomson and Tait, Natural Philosophy, vol. i., part i., sec. 326 to 
368, pp. 337-439- 



the previous history, reckoning from some chosen 
instant, as epoch. If we take the simplest case of a 
particle moving with constant velocity, and therefore 
with constant kinetic energy in a straight line, the 
Action is simply the kinetic energy multiplied by the 
time, and increases at a steady rate. If the particle is 
guided between two positions by any other than the 
straight line connecting these positions, it must describe 
a longer course and, since the speed is constant, take a 
longer time. In this simplest of all cases the minimum 
property is obviously fulfilled when the path pursued 
is the natural path. 

As already indicated, the principle of least action, 
taken in connection with the principle of the con- 
stancy of the sum of the potential and kinetic energies, 
leads to the equations of motion of the system under 
consideration. But it is only in problems of abstract 
dynamics that the sum of the potential and kinetic 
energies is constant. With the recognition of the 
true nature of heat came the great modern generalisa- 
tion of the conservation of energy. Heat is a form 
of molecular and ethereal energy ; and dynamically 
this great doctrine of the conservation of energy is 
the earlier principle of the constancy of the potential 
and kinetic energies, if cognisance be taken of the 
invisible motions of molecules and ether as well as of 
the visible mass motions. 

The idea of Helmholtz was to apply the principle 
of action to these wider problems. In the general 


dynamical system considered by him, the internal 
forces are assumed to be conservative, but the external 
forces depend on the time and work done by them and 
can be specially calculated. 

Helmholtz based his investigations on two functions 
of the co-ordinates and the velocities, namely, Hamil- 
ton's Principal Function, and the total energy. The 
total energy is the sum of the potential and kinetic 
energies, while the Principal Function (called by 
Helmholtz the Kinetic Potential] is the difference of 
these two quantities. The principle of least action 
was then defined in these words : If calculated for 
equal short intervals of time, the negative mean value 
of the kinetic potential, while the system passes by its 
natural path from one configuration to another, is a 
minimum as compared with its value by all other 
contiguous paths described in the same time from the 
initial to the final configuration. For cases of equili- 
brium, the kinetic potential becomes the potential 
energy ; and the principle just enunciated becomes 
the well-known condition for stable equilibrium, 
namely, the potential energy must be a minimum. 
From the minimum theorem of the kinetic potential, 
Helmholtz then deduced the principle of the constancy 
of energy, and applied the principle to important 
general problems in thermodynamics and electro- 
dynamics. He considered that the truth of the 
principle went far beyond the dynamics of ponderable 
masses, and that it was the general law for all reversible 


processes in nature ; while, in regard to irreversible 
processes as, for example, in the generation and con- 
duction of heat the irreversibility appeared to depend, 
not upon the essential nature of things, but upon the 
limitation of our powers in reducing to order again 
haphazard motions of molcules, or in reversing the 
molecular movements associated with the transference 
of heat. 

The outcome of this discussion is to show that in 
the mechanical operations of nature, there is simplicity 
and economy. The members of a system, free to 
move amongst each other, and unaffected by any 
external system, may have many paths along which 
they might pass from one position to another, so as 
to make a change from one configuration to another, 
but they always travel by the best possible route, and 
thus bring about the change in a simple way. What 
the real significance of this is we do not know, and 
we must eliminate from the conception the notion of 
choice. It may yet be shown why this must be so. 
This principle, apparently, has universal application, 
and it is the guide in many investigations. 

In his paper on Maxwell's theory of movements in 
the free ether, already referred to (p. 219), Helmholtz 
plunges into questions of an extremely difficult nature, 
and on which all his powers of mathematical analysis 
and his capacity of wielding, like an intellectual Titan, 
the tremendous principles of the conservation of energy 
and of least action, are brought to bear. Ponderable 


matter is everywhere bathed by ether and is permeated 
by it. If the ponderable matter and the ether are in 
close grip one with the other, one may reason from the 
movements of the former to those of the latter. But 
if we consider the spaces which are empty of ponder- 
able bodies and filled with ether alone, then the 
question arises, has the ether any inertia ? Again, 
suppose ponderable bodies move in the ether, can the 
latter get out of their way, or does it pass through 
the ponderable bodies like water through a sieve, or 
does the ether remain at rest or is it partly dragged 
along by the ponderable bodies ? Helmholtz finds, 
on the assumption that ether is an incompressible 
frictionless fluid, having no inertia, that the electro- 
magnetic law of Clerk Maxwell, experimentally 
proved by Hertz, holds good, and explains all the 
phenomena. He finally draws important conclusions 
as to the character of the discontinuity at the 
boundary of ether and ponderable matter, and the 
manner in which the electrical and magnetic forces 
originate. This paper was a fitting termination to 
the labours of Helmholtz in the lofty region of 
mathematical physics. 




TO understand the position of Helmholtz, with 
regard to the great questions in philosophy, 
we must take into account the school in which he 
was trained and the path which he chose for himself in 
physiological investigation. No physiological principle 
influenced him so much as that of the specific energy 
of nerves, taught by Johannes Miiller. The statement 
of this principle is, that in whatever way a terminal 
organ of sense may be stimulated, the result in con- 
sciousness is always of the same kind. Thus the 
vibrations of the ether that constitute physical light, 
or pressure, or electrical stimulation, all cause, when 
applied to the retina or to the optic nerve, sensations 
of luminosity. The same is true of all the sense 
organs. It is evident, therefore, that there is no 
correspondence between the sensation and the physical 
nature of the stimulus arousing it, seeing that the 
latter may be varied while the former remains un- 
altered. This principle was the guide to Helmholtz 
in all his physiological work on the senses, just as that 


of the conservation of energy controlled and directed 
him in the sphere of physical research. Lotze has 
finely said, that philosophy is always a piece of life, and 
that a prolonged philosophical labour is nothing else 
but the attempt to justify, scientifically, a fundamental 
view of things which has been adopted in early life. 1 
This is well illustrated in the case of Helmholtz. 

He early adopted a system of empiricism, and was 
thus, in a modified sense, a follower of John Locke, the 
English philosopher who denied the existence of innate 
ideas. Nothing is in the intellect except what came 
by sensory impressions, and, to begin with, the mind 
was a tabula rasa, a blank tablet, ready to receive the 
inscriptions of the outer world. Knowledge was 
derived from sensuous perception, or sensation, and 
partly from internal perception or reflection. Ex- 
ternal objects were appreciated by the senses, while 
within there was the apprehension of psychical 
phenomena by a kind of internal sense. All spatial 
properties had objective reality, but sensible qualities, 
such as sound, colour, taste, were in the perceiver and 
not in the objects themselves. Sensations were signs 
or symbols, not copies of the external things. They 
are no more like the real thing than words are like 
the ideas they represent. In the inner world of mind 
reflection enables us to know the actions of our 
willing and thinking faculties. From the two 

1 Philosophy of the Last Forty Years. Contemporary Review, Jan. 

2 5 I 


sources of knowledge, the internal and external, we 
obtain ideas, which may be simple or complex, and 
ideas always deal with modes, substances or relations. 
It is clear, therefore, that our knowledge, accord- 
ing to these doctrines, must be mainly gained from 

Spinoza, Descartes and Leibnitz, on the other 
hand, held that the mind, by its own powers, could 
transcend the limits of experience and reach the truth. 
The pantheistic monism of Spinoza implied unity of 
substance, this substance having the fundamental 
qualities of thought and extension ; God, ourselves, and 
the world were one. A mode of extension (an ex- 
ternal object), and the idea of an object are, in the 
language of Spinoza, the same thing expressed in 
two different ways. To understand a sensory im- 
pression we must have an idea of the affected as 
well as of the affecting body. 

Descartes conceived all external bodies to be ex- 
tended substances, while the soul is a thinking sub- 
stance without extension. External bodies are real, 
because we are conscious of the dependence of sensa- 
tions on external causes. Soul and body interact, 
touching at one point, the pineal gland, and thus 
body and spirit constitute a dualism, but the mode 
of interaction is incomprehensible. Why did Des- 
cartes attach such importance to an obscure little 
organ, now known to be an abortive eye ? Leibnitz 
introduced his strange system of monads, a monad 


being a simple unextended system, having power 
of action. Active force is the essence of substance. 
Monads are like the atoms of Democritus, they 
are centres of force, a notion not unlike the modern 
conception of Lord Kelvin, which describes atoms 
as rotational movements of the ether. But we part 
company with modern notions when we meet with 
the assertion of Leibnitz, that the active forces in 
monads are ideas. The soul is a monad, for it can 
act on itself, a proof of its substantiality. Every 
finite monad has a perception of those parts of the 
universe to which it is related ; to our sensory per- 
ceptions, the order of the monads appears as the 
temporal and spatial order of things, while time is 
the order of succession of phenomena. There is a 
pre-established harmony between the movement of the 
monad and the ideas of the mind, itself a monad. 
Mind and body work together like two clocks, set 
together and moving at the same rate. 

Much controversy arose between the schools of 
Locke and Leibnitz, and the battle raged with varying 
fortunes until Kant threw his influence on the side of 
the latter. The origin, extent and limits of know- 
ledge were examined in his Critique of the pure reason, 
by the latter meaning reason independent of experi- 
ence. He established the twelve categories or original 
conceptions of the mind, unity, plurality, totality, 
reality, negation, limitation, substantiality, causality, 
reciprocal action, possibility, necessity, existence, as 


the forms by which judgments are conditioned. He 
also made the important distinction between judgments 
a posteriori and judgments a priori. A judgment 
a posteriori is founded on experience. On the other 
hand, a judgment a priori is one having the marks of 
universality and necessity. Thus the latter judgments 
are either absolutely independent of experience, or they 
are relatively independent, in the sense that the con- 
ceptions employed are deduced from other conceptions 
which had been previously derived from experience. 
He assumes that the necessity and universality of a 
priori judgments cannot arise from any combination of 
experiences. Again, he draws a distinction between 
analytical and synthetical judgments. If by analys- 
ing the conception of the subject we find the predicate, 
or if the subject and the predicate are identical, the 
judgment is analytical ; but if the conception of the 
subject does not contain the predicate, so that the 
latter must be added to it, the judgment is synthetical. 
Synthetic judgments fall into two classes : those 
synthetic a posteriori^ in which the synthesis of subject 
and predicate is effected by experience ; and those 
synthetic a priori^ if the synthesis occurs apart from all 
experience. Some a priori judgments are thus 
synthetic, such as those of mathematics. The funda- 
mental judgments of arithmetic, such as 6 = 6, are 
analytic, but all those of geometry, such as the so- 
called axioms of Euclid, have the marks of strict 
universality and necessity, and are synthetic a priori. 


He places in the same group even general physical 
conceptions, such as the indestructibility of matter. 
Such statements, according to Kant, are true apart 
from all experience. In like manner the law of 
causality, our conceptions of time and space, our con- 
ceptions of space in three dimensions, are of tran- 
scendental origin, we possess them a priori, they are 
born in us, or, to use the technical word, they are 

Helmholtz was early brought into collision with 
this aspect of Kant's philosophy. It seemed to him to 
imply that some conceptions came from without, or, 
rather, that they were placed in the mind by an 
external or supernatural power, an implication that 
conflicted with the scientific view of the universe. 
In the tract on the conservation of energy, Helmholtz 
asserts 'that Science, whose object is to understand 
nature, must start from the assumption of its intelligi- 
bility.' In other words, nature must explain herself, 
and she must hold all the contents necessary for an 
explanation of everything. His subsequent physio- 
logical studies, more especially those on the senses, led 
him to different notions as to the way, for example, 
in which an animal becomes cognisant of the outer 
world. It does so by the use of its sense organs and 
by the movements of its limbs. The latter are at first 
apparently purposeless, but, by a kind of education, 
they are brought into relation with sensory impressions. 

He appears, however, to have felt the force of the 


objection to the empiristic view of things that some 
animals, when newly ushered into the world, seem 
already to possess a large amount of knowledge. He 
remarks : * The accuracy of movement of many 
new-born animals, or of those who have just escaped 
from the egg, is very striking ; the less mentally 
endowed these are, the sooner do they learn all they 
can possibly learn. The newly-born human child, 
on the contrary, is very slow in acquiring visual 
perception ; it takes several days to learn how to 
judge as to the way in which it has to turn its 
head to reach the mother's breast. Young animals 
seem to be more independent of individual experience. 
But what this instinct is which guides them may be 
.... those are matters of which as yet we know 
practically nothing (dariiber wissen wir Bestimmtes 
noch so gut wi nichts).' 1 

This matter, however, does not seem so inexpli- 
cable in the light of the Darwinian hypothesis, with 
which Helmholtz often expressed his general agree- 
ment. If the origin of an eye or an ear can be so 
far explained by the Lamarckian principle of the 
adaptations of an organ to its environment, and if this 
be supplemented by the law of variation and sur- 
vival of the fittest, it does not seem difficult to 
explain the gradual accumulation of experiences 
through countless generations leading to the forma- 

by Du Bois Reymond. Gtdachtnissrede, s. 39. Berlin, 

2 5 6 


tion of what are termed instinctive habits. Thus 
we may account for the origin of even a priori 
conceptions. These seem to be so universal, so true 
when stated, that the element of experience in their 
formation is overlooked. In this way the mind is 
not a clean tablet, as supposed by Locke, but it is 
a tablet already modified by the accumulated experi- 
ences of a pedigree. The great difficulty met with 
in such lines of thought, is the question of why 
modifications go on in a particular line and appar- 
ently with a determinate end ? Why are organs 
modified in a particular direction ? why has the 
physical subtratum of mind been gradually so 
built up that certain statements, and not others, are 
recognised as intuitive ? The evolution hypothesis, 
while it may apparently reconcile the empiristic and 
nativistic views of the origin of certain conceptions, 
as held by Spencer and Du Bois Reymond, does not 
explain the whole matter. It is certainly difficult, 
as stated by Du Bois Reymond himself, to reconcile 
with the empirical theory the fact that a butterfly 
only just escaped from the larval state should, during 
its short existence as it flits from flower to flower, 
apparently recognise and know, as if from experience, 
space in its three dimensions, the resistance of the air, 
the feeling of falling, and be able to discriminate the 
colours of flowers. As it could not have gathered 
experience of these things during its lowly life as a 
caterpillar on a cabbage leaf, in what stage or stages 


of its ancestral existence did it acquire this experi- 
ence ? We may be able to answer this question 
when we have full knowledge of the whole evolution 
of insect life, but at present it is a mystery. It is 
still more difficult to understand, on the empiristic 
theory, how the human infant, during the first three 
months of its life, learns to use its hands and eyes 
for a definite purpose. Does it begin to acquire 
knowledge by a series of more or less successful ex- 
periments, or is there something even here, acquired by 
long ancestral experience, that tells the child it need 
not try to grasp the moon, while it makes a mistake 
with the gaslight near it and burns its little fingers ? 
Helmholtz supported the empiristic point of view 
by questioning the correctness of Kant's ideas as to 
the nature of space, and the a priori truth of the 
axioms of geometry. As early as 1852, while in 
Konigsberg, at the very university in which Kant 
lectured for many years, Helmholtz published an 
important lecture on the nature of human sensa- 
tions. 1 Then he critically examined such questions, 
in the last section of his work on physiological optics, 
laying down the fundamental proposition, that sensa- 
tions are for consciousness only signs, the interpretation 
of which is given by the intelligence. For vision, 
these signs give intensity, quality (colour), and, in 
relation to the part of the retina affected, what he 
terms the local sign, that is the apparent position. 

1 Witftnschaftl. Abhandlungen, Bd. ii., 8. 591. 
2 5 8 


Notions of extent and of movement are not derived 
necessarily from visual perceptions, but from the 
feeling of movement due to muscular contractions, 
and even to the degree of innervation felt to be 
necessary for a particular movement. Other im- 
pressions are added to those of the visual organs ; 
thus the eyes or head are moved so as to see the object 
in different positions ; it is touched, etc., and the 
ensemble of all possible sensations gives rise to the 
representation of the object to the mind. This is 
perception, when applied to actual sensations, or it 
may be a representation due to memory. The 
psychical act is the association of the signs derived 
from the organs of sense, or the association of re- 

In 1866, two elaborate papers appeared on the 
axioms of geometry ; a synopsis of these was placed 
before English readers in 1870 ; I there was a popular 
lecture on the same subject in 1876; in the same 
year, and in 1877, two papers were published on 
the origin and meaning of geometrical axioms, 2 
and in 1894, the year of his death, a last 
paper on the accurate explanation of sensory im- 

There can be no doubt the researches of Helm- 
holtz into the phenomena of single vision with two 

1 The Academy >, vol. i., p. 128. 

2 Mind, vol. i., p. 301 ; also vol. iii., p. 212. 

3 Zeitsch.fur Psychologic und Physiologic der Sinnesorgane, Bd. 7, s. 18. 



eyes, the theory of corresponding points, and the 
mathematical investigation of the geometrical form 
of the horopter in different circumstances, led 
Helmholtz to question Kant's doctrine of space. 
The philosopher of Konigsberg taught that space 
and time are forms of intuition. Space is the form of 
external sensibility, that is our sense of the relative 
positions of things in the outer world ; while time 
is in the form of internal and external sensibility 
jointly, that is our sense of the relative sequences 
of events. On the a priori nature of space depends 
the validity of geometrical judgments. On the a 
priori nature of time arithmetical judgments depend. 
Things in themselves related neither to space nor 
to time are unknowable to man. Co-existence and 
succession are only in phenomena and are only in 
the perceiving subject. Now Helmholtz found in 
the study of the horopter, that two different sensa- 
tions arising from the picture on each retina are 
blended together in consciousness, that this blending 
cannot be anatomically explained, and, indeed, has 
no anatomical foundation, and that it is due to a 
mental act, which is the result of experience. We 
cannot separate the part due to the immediate sen- 
sation from the part due to experience. There is 
not a perfect agreement between the external object 
and the mental representation, except in a mathe- 
matical sense. The feeling of localisation in space 
is not inborn, but is the result of an act of reason 


or intelligence. It is not necessary to establish a 
harmony between local visual signs and certain corre- 
sponding positions in space, but there is a harmony 
between the laws of representation and of thinking 
and those of the outer world. 

Among the elementary propositions of geometry 
there are some that are held not to require proof. 
There are the axioms, such as, (i) if the shortest 
line drawn between two points is called straight, 
there can be only one straight line ; (2) through 
any three points in space, not lying in a straight 
line, a plane may be drawn, that is, a surface which 
will include every straight line joining any two of 
its points ; and (3) through a point lying without 
a straight line only one straight line can be drawn 
parallel to the first ; so that two straight lines that 
lie in the same plane and never meet, however far 
they may be produced, are called parallel. Again 
there are such propositions as that a solid is bounded 
by a surface, a surface by a line, and a line by a 
point ; that the point is indivisible, that by the 
movement of a point a line is described, by that of 
a line a line or a surface, by that of a surface a 
surface or a solid, and by the movement of a solid 
a solid and nothing else is described. 1 The question 
arises, how far results of experience have become mixed 
up with logical processes ? Now, in problems of geo- 
metrical construction, these axioms are true in all 

1 Mind, vol. i., p. 302. 


conceivable circumstances. The Euclidean method 
of proof is to establish the congruence of lines, 
angles, plane figures, solids, etc., and this is done 
by applying the one figure to the other, without 
changing their form or dimensions. But the method 
of establishing congruence implies mechanical move- 
ments, and by mechanical movements we acquire 
experience. If so, every proof of congruence rests 
upon experience. 

To illustrate this point of view, Helmholtz imagines 
beings with perceptions like our own living in worlds 
differing from our own. The mind can readily con- 
ceive beings of two dimensions living on a plane 
surface, and so confined to it, that they had no 
power of perceiving anything outside this sur- 
face. The geometry of such beings would show 
that the movement of a point described a line, and 
that of a line described a surface ; but they could 
not even imagine the form produced by the surface 
moving out of itself, so as to describe say a 
sphere or a cone. Living on an infinite plane, 
their geometry would be like planimetry. Again, 
we can conceive of intelligent beings living not on 
a plane but on the surface of a sphere. Their 
shortest line would then be an arc of the great 
circle passing through its ends. On a plane there 
could be only one shortest line between any two 
points, and in general this is also true of two points 
on a spherical surface, except when the two points 


are diametrically opposite one another, in which case 
an infinite number of shortest lines (/.<?., great 
circles) can be drawn between them. Sphere- 
dwellers, as Helmholtz calls them, would know 
nothing of parallel lines ; they would say that two 
'straight' (portions of great circles) lines, sufficiently 
produced, must cut in two points, or form parts of the 
same 'straight' line. The sum of the angles of a 
triangle would always be greater than two right 
angles, increasing as the surface of the triangle became 
greater. Helmholtz also imagined the geometry of 
intelligent beings living on the surface of an egg- 
shaped body, or rather we must think of egg-shaped 
space. They would find it impossible to construct 
two congruent triangles at different parts of the 
surface. A triangle constructed near the pole would 
not be congruent with one at the equator. The 
periphery of a circle described at the blunt end of 
the body would be greater than that at the narrower, 
although the radii were equal, the radii being always 
measured by shortest lines on the surface. He then 
discusses the geometry of what is called a pseudo- 
spherical surface (a curious surface, of which a strip 
may be represented by the inner surface turned 
towards the axis of a solid arch or ring, the curves 
of which are infinitely continued in all directions). 
Such a surface was first investigated by Beltrami. 
The straightest lines df the pseudo-sphere may be 
infinitely produced, but they do not, like those 


of a sphere, return on themselves. On such a 
surface, also, as on a plane, only one shortest line 
is possible between any two points, but the axiom 
as to parallels does not hold good. Like the 
plane and the sphere, it has its measure of curva- 
ture constant, so that figures constructed on one 
part of the surface can be transferred to any 
other place with perfect congruence of form and 
perfect equality of all dimensions lying on the 

It can also be shown, by a method devised by 
Riemann, that the space in which we live is three- 
fold, a surface is two-fold, and a line is an aggregate 
of points. Time is also an aggregate of one dimen- 
sion. Colour is an aggregate of three dimensions, 
because each colour may be represented by a mixtuie 
of three primary colours, taken in definite proportions, 
as may be shown by Clerk Maxwell's colour top. 
But Helmholtz goes still further. He shows that we 
can depict the appearance of a spheric or of a pseudo- 
spheric world, or such a world as we see in a con- 
vex mirror. Suppose we looked at things through 
specially-constructed convex glasses, we would at 
first be confused, more especially by illusions of com- 
parative size and distance, but, by experience, the 
space would cease to be strange. It is clear, there- 
fore, according to this argument, that the axioms of 
geometry do not all hold good in different varieties 
of space. Taken by themselves out of all connection 


with mechanical propositions, they represent no rela- 
tions of real things. c When thus isolated, if we regard 
them with Kant as forms of intuition transcendentally- 
given, they constitute a form into which any empiri- 
cal content whatever will fit, and which therefore 
does not in any way limit or determine beforehand 
the nature of the content. This is true, however, 
not only of Euclid's axioms, but also of the axioms 
of spherical and pseudo-spherical geometry. As soon 
as certain principles of mechanics are conjoined 
with the axioms of geometry, we find a system of 
propositions which has real import, and which can 
be verified or overturned by empirical observation, 
or from experience it can be inferred. If such a 
system were to be taken as a transcendental form 
of intuition and thought, there must be assumed 
a pre-established harmony between form and 
reality.' x 

In our space of three dimensions, we can give up, 
as it were, what we possess, and be able to imagine 
a space of two dimensions inhabited by creatures 
having no thickness, and living between two layers 
infinitely close together, so that they could move 
from side to side and backwards and forwards ; or 
a space of one dimension, like a tunnel, in which 
creatures having no thickness and no breadth could 
move only backwards and forwards. We cannot, 
however, go the other way and conceive a space of 

1 Mind, vol. i., p. 321. 


four dimensions, because we have no organs by which 
such a conception can be formed ; but it does not 
follow that there may not exist space of four dimen- 
sions, or, indeed, of any number of dimensions. If 
anything we saw slipped into the fourth dimensional 
space it would vanish from our eyes, and we 
would be quite unable either to follow it or to 
imagine whither it had gone. The point, however, 
is, that intelligent creatures living in a two-dimen- 
sional or in a one-dimensional space could develop 
a geometry of their own, in which the axioms would 
be like our own Euclidean axioms. Further, such 
intelligent beings living on a spherical or a pseudo- 
spherical surface, in which Euclidean axioms do not 
hold good, might develop a spherical or a pseudo- 
spherical geometry. Such non-Euclidean geometries 
have actually been worked out in some detail by 
Lobatschewsky of Kasan, and Beltrami of Bologna. 
Helmholtz, from these mathematical speculations, 
concludes : ( i ) that Kant's assumption of the a priori 
nature of the axioms is not proved ; (2) that it is 
unnecessary ; and (3) that it is useless for the explana- 
tion of the real world. Still he takes care not to 
deny that space may be transcendental, even although 
the axioms of geometry may not be so, but are 
ultimately founded on our experience of the state of 
things in the space in which we live. The axioms 
then are empirical and are derived, like other laws of 
nature, from observation and induction. Helmholtz, 


however, admitted that the law of causality is tran- 
scendental. 1 

In a later paper, written in 1888, dedicated to 
Eduard Zeller on the occasion of his jubilee, Helm- 
holtz endeavoured to disprove that the axioms of 
arithmetic were also a priori truths. 

1 For a criticism of Helmholtz's papers on the axioms of geometry, 
the reader is referred to a paper by W. Stanley Jevons in Nature, vol. iv., 
p. 481, 1871. See also Helmholtz's lecture on The Origin and Significance 
of Geometrical Axioms. Lectures, 2nd series, p. 27. London, 1881. 




^ I ^HERE is still one department of human 
J- thought in which Helmholtz made his mark. 
His manifold studies in the physiology of vision and 
of hearing brought him into relationship with the 
principles of art, and with that branch of philosophy 
which we include under the name of aesthetics. He 
was a lover of art in all its forms, and the contempla- 
tion of works of art was one of his favourite recrea- 
tions. The writings of Kant, Schelling, Hegel, and 
Schopenhauer on art were familiar to him, and 
although he did not agree with the metaphysical 
conceptions on which many of their notions were 
founded, his writings show that they exercised an 
important influence on his ideas. On the whole, his 
notions as to what constitutes the beautiful lean to 
those of Kant, namely, that the beautiful, through 
the harmony of its form with the faculty of know- 
ledge, awakens a disinterested, universal, and necessary 
satisfaction. Art is not merely the pleasure of the 
senses ; it has in view the feeling of pleasure, but it 
always implies judgment. It must be free from 


the restraint of arbitrary rules, as if it came from 

' No doubt,' he says in summing up the results of 
the volume on Sensations of Tone, c is now entertained 
that beauty is subject to laws and rules dependent on 
the nature of human intelligence. The difficulty 
consists in the fact that these laws and rules, on 
whose fulfilment beauty depends, and by which it 
must be judged, are not consciously present to the 
mind, either of the artist who creates the work, or 
the observer who contemplates it. Art works with 
design, but the work of art ought to have the appear- 
ance of being undesigned, and must be judged on 
that ground. Art creates as imagination pictures, 
regularly without conscious law, designedly without 
conscious aim. A work, known and acknowledged 
as the product of mere intelligence, will never be 
accepted as a work of art, however perfect be its 
adaptation to its end. . . . And yet we require 
every work of art to be reasonable, and we show 
this by subjecting it to a critical examination. . . . 
The more we succeed in revealing the harmony and 
beauty of all its parts, the richer we find it, and we 
even regard it as the principal characteristic of a great 
work of art that deeper thought, reiterated observa- 
tion, and continued reflection show us more and 
more clearly the reasonableness of all its individual 
parts.* I 

1 Sensations of Tone, p. 569. 


Helmholtz also recognised the ethical importance 
of art, or rather, as expressed by Herbart, that ethics 
constituted a, perhaps the most, important part of 
aesthetics. Kant also held that the beautiful claims 
the assent of all as a symbol of the morally good. 
Helmholtz writes, * Remembering the poet's words 

Du gleichst dem Geist, den du begreifst, 1 

we see that those intellectual powers which were at 
work in the artist are far above our conscious mental 
action, and that, were it even possible at all, infinite 
time, meditation, and labour would have been necessary 
to attain by conscious thought that degree of order, 
connection, and equilibrium of all parts and all 
internal relations, which the artist has accomplished 
under the sole guidance of tact and taste, and which 
we have in turn to appreciate and comprehend by our 
own tact and taste, long before we begin a critical 
analysis of the work. It is clear that all high 
appreciation of the artist and his work reposes 
essentially on this feeling. In the first we honour 
a genius, a spark of divine creative fire, which far 
transcends the limits of our intelligent and conscious 
forecast. . . . Herein is manifestly the cause of that 
moral elevation and feeling of ecstatic satisfaction 
which is called forth by thorough absorption in 
genuine and lofty works of art. We learn from them 

1 Thou art like the spirit thou conceivest. 


to feel that even in the obscure depths of a healthy 
and harmoniously-developed human mind, which are 
at least for the present inaccessible to analysis by con- 
scious thought, there slumbers a germ of order that 
is capable of rich intellectual cultivation, and we 
learn to recognise and admire in the work of art, 
though executed in unimportant material, the picture 
of a similar arrangement of the universe, governed 
by law and reason in all its parts. The contempla- 
tion of a real work of art awakens our confidence 
in the originally healthy nature of the human 
mind when uncribbed, unharassed, unobscured and 
unfalsified.' I 

In a series of lectures delivered in Cologne, Berlin, 
and Bonn, and summarised in a paper on the relation 
of optics to painting, 2 he demonstrates the limitations 
imposed on truth to nature in artistic representations. 
He shows how the painter finding that binocular 
vision shows the flatness of a picture, carefully selects, 
partly the perspective arrangement of his subject, its 
position, and its aspect, and partly the lighting and 
shading, in order to give an intelligible image of its 
magnitude, shape and distance. He illustrates the 
condition of securing a truthful representation of 
aerial light, and how to transform the scale of 
luminous intensity so as to secure proper shading of 
colour. He then writes, * The artist cannot tran- 
scribe nature ; he must translate her ; yet this 

1 Sensations of Tone, p. 571. * Lectures, p. 73. London, 1 88 1. 

2 7 I 


translation may give us an impression in the highest 
degree distinct and forcible, not merely of the objects 
themselves, but even of the greatly altered intensities 
of light under which we view them. ... If in 
these considerations, my having continually laid 
weight on the lightest, finest, and most accurate 
sensuous intelligibility of artistic representation, may 
seem to many of you as a very subordinate point, 
a point which, if mentioned at all by writers on 
aesthetics, is treated as quite accessory, I think this 
is unjustly so. The sensuous distinctness is by no 
means a low or subordinate element in the action 
of works of art ; its importance has forced itself the 
more strongly upon me the more I have sought to 
discover the physiological elements in their action.' 

This brief statement contains an expression of the 
main aesthetical principles enforced by Helmholtz. 
The combination of qualities found in him was of the 
rarest kind, and it was fitting these qualities were 
brought to bear on such questions. Schelling wrote 
that science in its highest perfection has the same 
problem to solve as art, but the method of its 
solution is different. In science the method may 
be mechanical, and the possession of genius is not 
absolutely necessary, but genius alone can solve 
artistic problems. In Helmholtz we had all that 
science could teach, and all that genius could 




"pvURING his whole life Helmholtz was in the 
--' habit of giving occasional lectures of a popular 
character. He did not consider that it was a waste 
of his time or beyond his province, to lay before an 
intelligent audience of men and women in the middle 
ranks of life, the results of his own scientific enquiries. 
Lectures of this description were not common in 
Germany, and in this matter of popular exposition 
Helmholtz was one of the first to attempt the ex- 
periment. In a preface to a translation into German 
of the lectures of Tyndall, Helmholtz alludes to the 
fact that such lectures had long been given in 
England, and he defends the practice as being likely 
to stimulate thought and to awaken an interest in the 
work of scientific men. There can be no doubt that 
the so-called popular lectures of Helmholtz reach the 
high-water mark in this class of literature. Prepared 
with great care, fitly illustrated by experiment, 
delivered with dignity, they made a great impression 
in Germany, and indeed all over the world. The 


fame of Helmholtz has been extended by these lectures, 
which have brought instruction to the learned and the 
unlearned alike. In the printed form, and even in the 
translations, they are literary productions of great 
completeness. They give one a feeling of thorough- 
ness in the treatment of the subject. The matter is 
discussed by a master, who brings to bear upon it all 
his wealth of learning and research, while there is the 
ever-enduring interest that attaches to an exposition 
by one who is giving forth from his own treasury. 
The lectures of Helmholtz are the fruit of his own 
thought and labour. They do not amuse ; they 
instruct, and they inspire. They are usually on 
difficult subjects, and they take a wide and com- 
prehensive survey. In the popular exposition of the 
phenomena of vision, of hearing, of the qualities of 
musical tone, of colour and the art of painting, Helm- 
holtz stands, in his own field, head and shoulders above 
all his contemporaries. 

The lecture on Goethe, delivered in 1853, is 
specially worthy of notice. 1 It was supplemented 
by a paper dealing with some aspects of the same 
subject, read in 1892 to the Generalversammlung der 
Goethe-Gesellschaft at Weimar. In this lecture he 
describes and explains the great poet's researches on 
colour, and shows the mental bias that completely 
led him astray in his theory of colour. At the 
same time he extols Goethe's scientific insight as 

1 Lectures, p. 33. London, 1873. 


shown in his speculations on the morphology of the 
skull and of the flower. Other great lectures are on 
sensory perceptions, on the eye and vision, on the 
relation of the natural sciences to knowledge, and on 
geometrical axioms. 

Worthy of notice also are his speech in memory 
of his great teacher Magnus, and a rectorial address 
on the academic freedom of the German universities. 
In the latter lecture there are several admirable 
examples of his way of thinking that are well worth 
quotation : 

I. German Student Life. 'The German student 
is the only one who tastes an unmingled joy at the 
time when, in the first delight of his young independ- 
ence, yet free from the anxieties of mercenary work, 
he may consecrate his hours exclusively to all that is 
noblest and best in science and in the conceptions 
of humanity. United by a friendly rivalry with 
numerous comrades devoted to the same efforts, he 
finds himself daily in intellectual communication with 
masters from whom he learns what is the movement 
of thought among independent spirits. I appreciate 
at its full value this last advantage, when, looking 
back, I recall my student days and the impression 
made upon us by a man like Johannes Miiller, the 
physiologist. When one feels himself in contact with 
a man of the first order, the entire scale of his intel- 
lectual conception is modified for life ; contact with 


such a man is perhaps the most interesting thing 
which life may have to offer.' 

2. Freedom. ' There is here for feeble characters a 
gift as calamitous as it is precious for the strong. . . . 
But the state and the nation have more to expect from 
those who are capable of supporting liberty, and whose 
efforts and work are the results of their own individual 
energy, of their dominion over themselves, and their 
love of science.' 

3. Professorial Fitness. ' The doing something for 
the progress of science is the best mark of a man's 
fitness to educate.' 

4. Use of Lectures. C A good exposition demands 
from the listener much less sustained effort than a bad 
one ; it enables the subject to be comprehended much 
more surely and much more completely, and with a 
well-ordered arrangement, bringing into strong relief 
the principal points and the divisions, much more can 
be overtaken in the same space of time.' 

5. Teachers. ' He who wishes to inspire his 
audience with a complete conviction of the truth of 
what he advances, ought, above all, to know from 
personal experience what produces conviction. It is 
necessary, then, that he should have known how to 
advance alone into a region where no one has ever 
broken ground ; in other words, he must have worked 
upon the frontiers of human science and conquered for 
himself new domains. A master who presents only 
results acquired by others, suffices for scholars to whom 



authority is given as the source of their science, but 
not for those who desire to deepen their convictions 
to their final foundations.' 

6. Judgment of Students. 'All this system rests 
upon the idea that the general current of the opinion 
of the students cannot long be at fault. The majority 
among them come to us with a reason sufficiently 
formed by logic, with a sufficient habit of intellectual 
effort, with a judgment so considerably developed by a 
knowledge of the best models, as to be able to discern 
the truth from a phraseology which has only the 
appearance of truth.' 

One of the greatest lectures given by Helmholtz 
is on Thought in Medicine, delivered on 2nd August 
1877, on the Anniversary of the Foundation of the 
Institute for the Education of Army Surgeons. 1 It 
opens with the following sentence : ' It is now 
thirty-five years since, on the 2nd of August, I stood 
on the rostrum in the hall of this institute, before such 
another audience as this, and read a paper on the 
operation for Venous Tumours. I was then a pupil 
of this institution, and was just at the end of my 
studies.' When he delivered the lecture on Thought 
in Medicine he was Professor of Mathematical Physics 
in the University of Berlin, and the foremost man 
of science in Germany. He adds : 4 1 rejoice, there- 
fore, that I can once more address an assembly, 

1 Lectures, p. 199. 1881. 


consisting almost exclusively of medical men who 
have gone through the same school. Medicine was 
once the intellectual home in which I grew up ; 
and even the emigrant best understands and is best 
understood by his native land.' 

It would be well if every young medical graduate 
throughout the world were presented with a copy of 
this lecture on the day of his graduation. 





T T ELMHOLTZ devoted much time and atten- 
J- A tion to the affairs of the Technical Institute 
during the last few years of his life. He was much 
esteemed and revered by the staff, whose reward was, 
as one of them said, a kind glance, or a pressure of 
the hand, or a word of appreciation from the master. 
His great mental gifts, his splendid record of work 
accomplished, and a certain nobility of nature impos- 
sible to describe, combined with a quiet, unobtrusive 
manner, brought tokens of regard for Helmholtz as 
the years passed onwards. The Emperor William I. 
often received Helmholtz in the domestic circle to 
discuss with him some of the more recent advances in 
science, and he was also in close intimacy with the 
Crown Prince Frederick (afterwards Emperor) and 
his Princess, both of whom took the deepest interest in 
everything relating to Art and Science. The Emperor 
William I. ennobled him, and in doing so conferred 
distinction not only on Helmholtz, but on the ranks of 
the peerage. Honours of many kinds flowed in upon 


him from all parts of the world. The celebration of 
his seventieth birthday became a national event, and a 
tribute was then paid to his eminence as a man of 
science and as an inspiring teacher, only equalled a few 
years ago by the ceremonies at the jubilee of his friend 
Lord Kelvin. The Emperor William II. sent him an 
autograph letter in ackowledgment of his great services 
to science, and conferred special honours upon him. 
The Kings of Sweden and Italy, the Grand Duke of 
Baden, and the President of the French Republic, 
sent him the insignia of various orders. Representa- 
tives of academies, universities, and learned societies, 
sent representatives and addresses. A Helmholtz gold 
medal was struck in his honour, to be awarded from 
time to time for distinguished services to science, and 
was, at a banquet, handed to Helmholtz himself as its 
first recipient, after a brilliant speech by his life-long 
friend Du Bois Reymond. At the same time a marble 
bust by Hildebrand was unveiled. 1 

At this banquet von Helmholtz delivered a speech, 
in which he uplifted the veil of his inner life and 
revealed some of the secret influences that contributed 
to his marvellous creativeness. His own words, in 
free translation, are better than any other. Referring 
to the medal, he said, 

4 It is the greatest honour men of science could pay 

1 On the 6th of June 1899, a marble statue of von Helmholtz was 
unveiled by the Emperor William II., in front of the University of 
Berlin. It has been fittingly placed near those of the brothers von 
Humboldt. See Daheim, 24th June 1899, No. 39, p. i. 


to me to connect my name with this medal, which 
will stamp the progress of science in future times. 
Science, to modern humanity, proclaims peace. The 
scientific man does not work for his own welfare, but 
for that of his nation, and for the whole of humanity, 
especially for those who are sufficiently educated to 
enjoy the fruits of science. You desire to associate 
my name with this medal, and to hold me up to 
coming generations as an example of an investigator. 
I waver between a feeling of joy and a feeling of grave 
responsibility. I have a proud joy that the result of 
my thoughts is to work on to future generations far 
beyond my individual life. You will also understand 
that as a father cares for his offspring, and endeavours 
to help them, so I have also a love for the children of 
my thoughts. These contain the best of my convic- 
tions ; I lay upon them the utmost stress ; and I 
rejoice if the further development of science is to be 
in their direction. But the doubt may arise, whether 
my own ideals are not too narrow, and my principles 
sometimes too imperfect, for the wants of humanity 
in all time. If so, I hope the awarders of this medal 
in the future will not confine themselves to what I 
have accomplished ; but I should like to wave on 
high the one banner on which are inscribed the 
words, that the purpose of science is to comprehend 
reality and the play of phenomena as regulated by 

On the occasion of his seventieth birthday, his eye 


was undimmed and his natural force was unabated, 
and it was hoped that he had yet many years before 
him to complete his life work by the publication of 
his lectures. He attended the meeting of the British 
Association for the Advancement of Science, in Edin- 
burgh, in 1892, and while years were evidently 
gathering upon him, his noble appearance made a 
deep impression on all who saw him. In 1893 he 
visited the International Exhibition in Chicago, and 
afterwards saw something of the grand scenery of 
North America and Canada. He then started on 
the homeward journey. Shortly before the steamer 
reached Hamburg he had an attack of giddiness, and 
fell down the stair of the cabin. The injury was 
severe, causing concussion of the brain and great loss 
of blood from a scalp wound. He recovered so far, 
but those about him saw strength failing. Now easily 
tired, work became more and more difficult. At last 
the brain that had worked so well gave way, and, in 
July 1894, he had a stroke of apoplexy. For two 
months he lingered on, showing, as one would expect 
from so great a nature, patience and calmness in look- 
ing forward to the end. This came on the 8th of 
September 1894, when he had lived eight days beyond 
his seventy-third birthday. 1 

1 In the Zeitschrift fur Psychologic of March 7th, Professor David 
Hansemann, of Berlin, published a report of his examination of the 
brain of Helmholtz. The circumference of the head was 59 centi- 
metres, that of the skull 55 centimetres. The breadth of the skull 
was 15-5, and its length 18-3 centimetres. The cephalic index was 


German artists have preserved for all time, in 
marble and on the canvas, Helmholtz's personal 
appearance. This appearance was an indication of 
his own inner strength. Rather above the middle 
stature, he had a firm, erect frame. His splendid 
head was well thrown back, so that his posture was 
always sure to command attention. The shape of 
the head was perfect, broad between the eyes but not 
out of proportion. The eyes 

* Such splendid purpose in his eyes ' 
were full of intelligence, not so brilliant as deep and 
reflective. They often had that far-away look so 
conspicuous in thinkers, as if the soul were away on 
its own quest. His manner was dignified, almost to 
coldness, but it was at the same time courteous. It 
is said that he had occasionally a peculiar look that 
caused a shallow man to stop asking questions and to 
feel his own unworthiness. With those who were 
truly in earnest he would take infinite pains to explain, 
listen to suggestions, and remove difficulties. Reserve 
was his habitual attitude. To his favourite students, 
and in the circle of his own friends, there was always 

therefore 85*25, showing a broad head. Helmholtz's head was about 
equal in size to that of Bismarck, and rather smaller than that of Wagner, 
both of whom had big heads. On the other hand, Darwin's head was 
only 56-3 centimetres in circumference. The weight of the brain, with 
its blood, was 1700 grams., without the blood, 1400 grams., being about 
100 grams, heavier than the average human brain. The sulci were very 
deep and well marked, especially in those parts of the brain which 
Flechsig has shown to be concerned in associations. The frontal con- 
volutions in particular were deeply cut by very numerous sulci. 


the charm of a great personality. The first time the 
writer saw him was in 1872, in the Gewandhaus, in 
Leipzig, during a performance of Mendelssohn's c Mid- 
summer Night's Dream.' Near the orchestra he saw 
a head of such splendid proportions, with the eyes 
having a rapt expression, as the sensuous music 
floated through the hall, and he thought ' that must 
be Helmholtz ! ' It could be no other. A few days 
later he saw the great physicist in his own laboratory, 
and received kindly advice regarding the ophthal- 
mometer and acoustical apparatus. 

Helmholtz was fond of mountaineering, and he was 
an excellent swimmer. Du Bois Reymond says that 
long walks, to which his father had accustomed him 
in the beautiful surroundings of Potsdam, had more 
than a hygienic value for him. Helmholtz himself 
tells us that it was often during walking that the 
solution of problems came before his mind. 

Volkmann, in his masterly estimate of the work of 
Helmholtz, remarks that one of his chief merits was 
to establish a harmony between the vast accumulation 
of facts that characterised the period comprehending 
the middle of this century and the more theoretical 
studies. The necessity for so doing was early felt by 
Helmholtz himself, for in 1874 we find him saying, 
4 It seems to me that it is not so much knowledge of 
the results of natural science which the wisest and 
best educated men seek, as an aspect of the mental 
activity of the investigator, a view of his scientific 


system, and a statement of the goal towards which he 
strives. They wish to know what his work has done 
for the great problems of human life.' 

Helmholtz indicates his position in the words he 
uses regarding his pupil Hertz. * He takes his place 
among those who see the advancement of humanity 
in the greatest possible development of their spiritual 
talents and in the sovereignty of the spirit over the 
natural passions and the hostile powers of nature. 
To bring about this there must be a severe mental 
discipline. Thought, the will, and the power of 
action must be brought into subjection.' Helmholtz 
himself submitted to a life-long discipline. He says : 
' I have never considered a research complete until 
it stood before me perfect and without logical defects. 
It was always formulated in writing. My conscience 
stood before my mind and the wisest of my friends, 
and I asked myself if they approved of my work. 
They were the embodiment of the scientific spirit of 
an ideal humanity and gave me my measure. 

' I do not mean to say that in the first half of my 
life, when I had still to work for my outward position, 
that higher ethical motives than those of the desire 
of knowledge, and a feeling of doing my duty as an 
officer of the state, influenced my life, at all events it 
was not easy to be sure of their existence while 
egoistic motives compelled me to work. Most in- 
vestigators feel this. But later on, when one's posi- 
tion had been secured, at a time when some who, 


having no inner propelling power towards science, 
cease to work, a higher aspect of one's relation to 
humanity came into the foreground. The thoughts 
that have found their way into literature, or into the 
minds of men by the teaching of pupils, continue to 
have an independent life ; these thoughts have further 
developments, and inspire teaching on newer lines. 
One's own thoughts are of course more in one's 
spiritual circle of vision than strange ones, and one 
feels satisfaction when he sees his own bearing fruit. 
Then a paternal feeling springs up in the mind of the 
thinker, and he cares and fights for the advancement 
of his offspring. Still, the whole world of civilised 
humanity is before him, the duration of whose life 
seems to be eternal in comparison with the short life 
of an individual. The investigator then sees himself, 
with his small contributions to the building up of 
science, in the service of an eternal sacred cause, to 
which he is bound by the closest bonds of affection. 
By this thought his own work is hallowed. To feel 
the full force of this, one must have had the experience.' 
Helmholtz, in a speech delivered at the banquet, tells 
us something of his mode of working. When a problem 
came before his mind he turned it round on all sides. 
He reflected upon it for several days, carefully thinking 
out the details of any experimental procedures that 
might be necessary. In the solution of more difficult 
questions, the light seldom came when he was at his 
desk, and never when the brain was fatigued. It was 


usually in the morning, after the wearied brain had 
been refreshed by sleep, or while walking up a hill- 
side, with pure air and bright sunny weather, that the 
truth flashed before his mental vision. Even the 
smallest amount of alcohol he found interfered with 
his mental work. He then reduced his views to writ- 
ing, and took great pains in giving correct expression 
to what he wished to communicate. In literary com- 
position he was extremely fastidious, often writing the 
manuscript six times over, and next day, even after 
this severe ordeal, he was never satisfied with what he 
had written. 

It is not necessary to define the position of Helm- 
holtz amongst scientific thinkers. His works bear 
their own evidence. There is a general consensus of 
opinion that he is one of the greatest men of the 
present century. To find one like him in mental 
power and width of range, we must go back to such 
intellectual giants as Descartes and Leibnitz, and 
even when he is compared with them, it must not be 
forgotten how enormously broader was the field of 
science in the time of Helmholtz than in the seven- 
teenth century. The only English philosopher with 
whom he may be compared is Thomas Young. 
Both were remarkable for versatility and originality ; 
both had the same wide range of knowledge ; both 
were manifold men of science ; both were physio- 
logists and physicists ; the researches of both were 
fundamental. But Helmholtz was, as a mathema- 


tician of the first rank, even greater than Young. It 
will be admitted that, taking him all in all, Helmholtz 
is the greatest Master of Medicine the world has ever 

Of Helmholtz's opinions on religious questions, 
nothing can be stated with any degree of precision. 
Such topics were not with him subjects of conversa- 
tion. But throughout his writings there breathes a 
spirit of reverence, while his noble and pure life is 
the highest testimony to his true worth. For such a 
man a time surely comes when 

* That in us which thinks and that which feels 
Shall everlastingly be reconciled, 
And that which questioneth with that which kneels.' 



STRONG soul, whose calm and almost God-like mien, 

Eyes of unfathomable depth of thought, 

And broad and lofty intellectual brow, 

Betoken force and insight : Shall I try 

To tread the path you followed in the quest 

Of Nature's truth ? To live in your great thoughts 

Is like to breathing a pure atmosphere 

On lofty mountain peak, in azure blue, 

While all around are pure white fields of snow, 

And all below is veiled in cloud and mist. 

And when I find atomic mazy dance, 

The swift-winged lightning, colour's sun-born hues, 

The tones of music and harmonious chords, 

Fine movements and the throb of nervous thrills 

That course so swiftly through this mortal frame, 

The hidden work of wond'rous ear and eye, 

Are all made clear and plain ; then comes the thought 

That He Who made all these did also send 

To this dull earth His own interpreter, 

A great and gifted intellect like thine, 

A child of genius, armed at every point 

For all the glorious work that thou hast done, 

Revealing Nature's plans ; and thou hast shown 

Man's soul is tuned to Nature, and reflects 

All things, as does the surface of a lake 

Reflect the glories of the earth and sky. 


1. Hermann von Helmholtz. Ein Nachruf von Dr J. 

Fernet, Professor der Physik am Eidgenossischen 
Polytechnicum. Neujahrsblatt der naturforsch- 
enden Gesellschaft, in Zurich, 1895. Zurich, 

2. Hermann von Helmholtz. Gedachtnissrede gehalten 

in der Singakademie zu Berlin am 14 Dezember 
1894, von Wilhelm von Bezold, mit einem 
Portrat nach einem Olgemalde von Franz von 
Lenbach. Leipzig, 1895. 

3. H. de Helmholtz. Esquisse biographique par le 

Dr E. Landolt. Archives d'Ophtalmologie, Decem- 
bre, 1894. 

4. Gedachtnissrede auf Hermann von Helmholtz, gehal- 

ten am 28 September 1894 in der Aula der 
Universitat Utrecht. Von Th. W. Engelmann. 
Leipzig, 1894. 

5. Hermann von Helmholtz. Gedachtnissrede von Emil 

du Bois Reymond. Leipzig, 1897. 

6. Hermann von Helmholtz. A Biography in Com- 

memoration of his joth Birthday, by Dr Hugo 
Kronecker, Professor of Physiology in the Uni- 
versity of Berne. Translated from the German by 
Dr Arthur Gamgee, F.R.S., Emeritus Professor of 
Physiology in the Owens College, Victoria Uni- 
versity, Manchester. Reprinted from The Elec- 
trician, August 2 1st and 28th, 1891. London, 1891. 


7. Hermann von Helmholtz's Untersuchungen iiber die 

Grundlagen der Mathematik und Mechanik. 
Rede zum Geburtsfeste des hochstseligen Gross- 
herzogs Karl Friedrich und zur akademischen 
Preisvertheilung am 22 November 1895, von 
Dr Leo Koenigsberger, Grossherzoglich Badischen 
Geheim-Rath und v. 6. Professor am Mathematik, 
d. z. Prorektor der Grossh. Bad. Universitat 
Heidelberg. Heidelberg, 1895. 

8. Ansprachen und Reden gehalten bei der am 2 

November 1891 zu ehren von Hermann von 
Helmholtz veranstalteten Feier, nebst einem 
Verzeichnisse der iiberreichten Diplome und 
Ernennungen sowie der Adressen und Gliick- 
wunschschreiben. Berlin, 1892. 

9. Hermann v. Helmholtz. Gedenkrede gehalten vor 

den v. Deutschen Mechanike lage zu Leipzig am 
21 September 1894, von Dr Hugo Kriiss. 
Vereinsblatt der Deutschen Gesellschaft fur Me- 
chanik und Optik, i Oktober 1894. No. 19. 
S. 146. 

10. Hermann von Helmholtz, von Hermann Munk. 

Sonderabdruck aus der Berliner klinischer Wochen- 
schrift, 1894. No. 38. 

11. Hermann v. Helmholtz, von J. Hirschberg. 

Deutsche medicinische Wochenschrift, 20 September 
1894. S. 733. 

12. Hermann von Helmholtz, von J. v. Kries, Professor 

der Physiologic zu Freiburg, i. B. Deutsche medicin- 
ische Wochenschrift. 27 August 1891. 8.1025. 

13. Hermann von Helmholtz. Reden gehalten bei der 

von der physikalisch okonomischen Gesellschaft 
zu Konigsberg in Pr. Veranstalteten Gedacht- 
nissfeier am 7 Dezember 1894, von Dr L. Her- 
mann, .ord. Professor der Physiologic, Geh. 
2 9 2 


Medicinalrath z. Z., President der Gesellschaft, 
und Dr P. Volkmann, ord. Professor der Theor- 
etischen Physik. Konigsberg, 1894. 

14. Obituary Notice of Hermann von Helmholtz, by 

Professor A. W. Riicker. Proceedings of the Royal 
Society, vol. lix., No. 355, p. 17. 

15. Notice of Hermann von Helmholtz, by Lord Kelvin 

in his Presidential Address at the Anniversary 
Meeting of the Royal Society, Nov. 30, 1894. 
Proceedings of the Royal Society, vol. Ivii., No. 340, 
p. 38. 

1 6. Ueber die Erhaltung der Kraft, eine physicalische 

Abhandlung. Berlin, 1847. 

17. Die Lehre von den Tonempfindungen physiologische 

Grundlage fur die Theorie der Musik. Braun- 
schweig, 1863-1870. 

1 8. Theorie physiologique de la musique fondee sur 

1'etude des sensations auditives. Traduit de 
I'Allemand par M. G. Gueroult. Paris, 1868- 

19. Sensations of Tone as a Physiological Basis for the 

Theory of Music. Translated by A. J. Ellis. 
London, 1875. 

20. Handbuch der physiologische Optik. Leipzig, 1 867. 

21. Optique physiologique. Traduit par Emile Javal 

et N. Th. Klein. Paris, 1867. 

22. Popular Lectures on Scientific Subjects. Trans- 

lated E. Atkinson. London, 1873. Second series, 

23. Das Denken in der Medicin. Berlin, 1878. 

24. Wissenschaftliche Abhandlungen. 3 Bande. Leipzig, 




25. Populare Wissenschaftliche Vortrage. Braunschweig, 


26. Handbuch der physiologischen Optik. Zweite 

ungearbeitete Auflage. Hamburg und Leipzig, 

27. Die Mechanik der Gehorknochelchen und des 

Trommelfels. Bonn, 1869. 

28. Titelverzeichniss sammtlicher Veroffentlichungen von 

Hermann von Helmholtz. Leipzig, 1895. 

29. Heinrich Hertz. Gesammelte Werke. 3 B'ande. Mit 

einem Vorwort von Hermann von Helmholtz. 
Leipzig, 1894-5. 

30. Hertz. Electric Waves, with preface by Lord 

Kelvin. London, 1893. 

31. Vorlesungen fiber theoretische Physik von H. von 

Helmholtz, herausgegeben von Arthur Konig, Otto 
Krigar-Menzel, Franz Richarz, Carl Runge. Band 
i.-vi. Leipzig. 



ACCOMMODATION, mechanism of, 7, i Bonn, Helmholtz on. 88. 

Action, at a distance, 203. 
Action, definition of dynamical, 245. 
Action, principle of least, 235, 240, 243. 
./Esthetics, Helmholtz on, 268. 
Aguilonius, reference to, 180. 
After images, 177. 

Bonn, University of, 129. 
Bowman, physiologist, reference to, 14. 
Boyle, Robert, reference to, 116. 
Branco, Professor, reference to, 58. 
Brewster, Sir David, reference to, 91, 
112, 118, no. 
British Association, Edinburgh meet- 

Air, micro-organisms in, 29. 

ing 1892, 282. 

Airy, reference to, 91, 118. 

British Association meeting at Hull 

Ampere, 210. 
Andrews, Thomas, reference to, 91. 
Apparatus, electrical, for physiology, 

1854, 9 1 - 
Briicke, early friendship with Helm- 
holtz, 10, n, 13, 24, 25, 74, 77, in. 


Brucke, on ciliary muscle, 101. 

Arm, muscles of, Helmholtz on, 170. 

Butterfly, life of a, considered em- 

Art, ethical importance of, 270 ; nature 
of, 269. 

pirically, 257. 

Axioms of geometry, Kant's opinions 

CAGNIARD DE LA TOUR, reference to, 

as to, 258. 


Cape d'Antibes, 192. 

BABBAGE, Charles, use of silvered 

Carnot, Sadi, reference to, 50, 194. 

mirror by, 77. 

Carpenter, reference to, 14. 

Bach, reference to, 167. 
Bacon, on heat, 46. 

Cayley, Arthur, reference to ( 190. 
Chicago, International Exhibition at, 

Baconian philosophy in Germany, 12. 


Baden, government of, 184. 
Baden, Grand Duke of, reference to, 

Chladni, plates of, 20. 
Ciliary muscle, 101, 102. 


Clang tint, 143. 

Balloons, steering of, and theory of, 

Clapeyron, on heat, 50. 


Clausius, physicist, 10, 23, 43, 194, 205. 

Beats, nature of, 156, 158. 

Clouds, Helmholtz on, 223. 

Beethoven, reference to, 134. 

Coccius, ophthalmoscope of, 77. 

Behr, reference to, 77. 
Bell, John and Charles, reference to, 

Cochlea, action of, 140, 141, 152. 
Coil.induction, of Du Bois Reymond, 36 


Colding, on energy, 50. 

Beltrami, reference to, 266. 

Colour blindness, 125. 

Bentley, reference to, 203. 
Berlin, Physical Society of, 24. 
Berlin, University of, 183, 239. 

Colour, Helmholtz's researches on, 112. 
Colour, nature of, 116. 
Combination tones, 159, 161. 

Bernard, Claude, reference to, 14. 
Bernoulli, Daniel, reference to, 40. 

Conservation of energy, 193, 242. 
Consonance, nature of, 156. 

Bertrand, reference to, 195. 

Cooper, Dr, reference to, 91. 

Bessel, reference to, 70, 202. 

Copernicus, reference to, 19. 

Bezold W. von, reference to, 218. 
Bibliography, 291. 

Corresponding retinal points, 173, 178. 
Corti, physiological action of the organ 

Binz, reference to, 182. 

of, 151, 154. 

Bismarck, head of, 283. 

Coulomb, reference to, 21 ; law of 

Bones of the ear, 133, 135. 

electrical attraction, 204. 



Cramer, on accommodation, 95. 
Critique of pure reason, Kant's, 253. 
dimming, W., reference to, 77. 
Currents, electrical, effects of those of 

short duration, in. 
Cuvier, reference to, 21. 
Cyclic systems, Hemholtz on, 234. 

D'ALEMBERT, reference to, 40, 52. 
Darwin, head of, 283. 
Darwin, reference to, 19. 
Darwinian hypothesis and innate ideas, 


Davy, Humphry, on heat, 47. 
De la Tour, Cagniard, reference to, 26. 
Democritus, reference to, 253. 
Descartes, 44, 46, 52, 96, 236, 252, 


Difference tones, 159. 
Dispersion, anomalous, 227. 
Dissipation of energy, 193. 
Dissonance, nature of, 156. 
Donders, reference to, 14, 82, 85, 97 ; 

reference to Cramer by, 97 ; on vowel 

tones, 162 ; on movements of eye- 

balls, 177- 

Dove, reference to, 22, 43, 181. 
Draper, reference to, 118. 
Drumhead, action of, 133, 135. 
Du Bois Reymond, reference to, u, 

15, 107, 108, 109, 118, 133, 135. 
Ductus cochleans, action of, 152. 
Dusch, reference to, 29. 
Dynamics, Helmholtz on principles of, 


EAR, bones of, 133, 135. 

Ear, damping arrangements in, 150. 

Ear, internal description of, 138. 

Edinburgh, reference to, 92. 

Electric interrupter, of Helmholtz, 


Electricity, animal, 66, 104. 
Electricity, theories of, 203 ; Helm- 

holtz's researches in, 209. 
Electrodes, non-polarizable, 105. 
Electrodynamics, 203. 
Empirical philosophy, 251. 
Encyclopaedists, reference to, 21. 
Energy, conservation of, 39, 193. 
England, Helmholtz's impressions of, 

Helmholtz on, 211, 222; on specific 
inductive capacity, 205. 

Fechner, reference to, 13. 

on, 26. 

Fermentation, studies by Helmholtz 

Erlach, Von, reference to, 74. 
Essex, reference to, 76. 
Ether, theory of movements in, 248. 
Euclid, anxioms of, 254, 262. 
Euler, reference to, 40, 114, 195, 237. 
Eyeballs, movements of, 171, 176. 
Eyeball, muscles of, 175. 
Eye, changes in ; in accommodation 
100 ; reflected light from, 73. 

FARADAY, reference to, 91 ; the lecture, I fations, 149 ^anomalous dispersion 

Fingal's Cave, reference to, 02. 

Fitness, professorial, Helmholtzon, 276. 

Fluid, nature of, 195. 

Fluids, discontinuity in, 201. 

Forbes, on ice, 221. 

France, intellectual life in, 21. 

Frederick the Great, reference to, 

Frederick, Crown Prince, reference to, 

Freedom, Helmholtz on, 275. 

French Republic, President of, refer- 
ence to, 280. 

Fresnel, reference to, 114. 

Frictionless fluids, 196. 

Friedrich Wilheim Institute, reference 
to, 40. 

Fourier's theorem, 144, 167. 

GALILE_O, reference to, 19, 38, 242' 
Galvani, reference to, 31. 
Gaugain, galvanometer of, 211. 
Gauss, reference to, 221 ; on unit of 

force, 239. 

Gay-Lussac, reference to, 27. 
Geometry, axioms of, 261, 
Geometry, non-Euclidean, 266. 
German student life, Helmholtz on, 

Germany, science in, during early part 

of igth century, 18. 
Goethe, reference to, 119, 221 ; lecture 

by Helmholtz on, 274. 
Goodsir, John, anatomist, reference to, 

Graefe, Von, reference to, 83. 

Grassman, reference to, 205. 

Grove, W. R., on condition of physical 

forces, 48, 91. 
Gruithuisen, reference to, 76. 

HALLER, reference to, 12 ; on rate of 

nervous impulse, 64. 
Hamilton, William Rowan, 91, 190, 

243 ; principle of varying action, 

Hansemann, David, reference to, 282. 
Harmonic tones, 147, 148. 
Hartley, reference to, 114. 
Hassenstein, on reflected light from 

eye, 74. 

Hay fever, Helmholtz on, 181. 
Heat, animal, 33. 
Heat, dynamical equivalent of, 49. 
Hegel, reference to, 20, 268. 
Helmholtz, Ferdinand, i 
Helmholtz, apparatus for phase re- 


230 ; as a lecturer, 273 ; as librarian, 
40 ; as a mathematician, 188 ; as a 
teacher, 130 ; birth of, i ; brain of, 
282 ; certificate from rector, 5 ; choice 
of medical profession, 9; closing 
years, 279 ; death of, 282 ; Director 
of Physico-Technical Institute, 185 ; 
early days as surgeon, 25 ; early 
friends, 6, 10 ; ennobled, 279 ; essay 
on energy, 40 ; first marriage, 58 ; 
second marriage, 187 ; general sketch 
of career ; 16 ; gold medal in honour 
of, 280 ; improvements on inductive 
coil, 37 ; inaugural thesis, 14 ; in- 
vestigations on electricity, 206 ; 
letter to Ludwig, 90 ; on animal 
heat, 33, 34 ; on art, 270 ; on cpn- 
bination tones, 160 ; on conservation 
of energy, 39, 53 ; on colours, 119, 
124 ; on Du Bois Reymond's theory 
of muscle current, 108 ; on empirical 
philosophy, 256 ; on fermentation, 
28 ; on hay fever, 181 ; on his own 
work, 286 ; on magnified movements, 
no; on muscular contraction, 33; 
on philosophy of Kant, 255 ; on 
physiological acoustics, 129, 131 ; on 
principle of least action, 246; on 
rate of nervous impulse, 59 ; on red 
and blue and green, 120 ; on relation 
of physics to physiology, 31 ; on 
superposition of spectra, 122 ; on 
vowel tones, 163 ; ophthalmoscope, 
71 ; parentage, i ; personal appear- 
ance, 283 ; personal characteristics, 
283, 287 ; philosophical position of, 
250 ; school days, 3 ; speech on re- 
ceiving medal, 280 ; speech when pre- 
sented with Von Graefe medal, 86 ; 
statue of, in Berlin, 280 ; student 
life, 8 ; surgeon to the Red Hussars, 
25 ; and Robert Mayer, 50. 

Helmholtz, Robert, reference to, 187. 

Herbart, reference to, 270. 

Hermann, Ludwig, reference to, 89. 

Hermann, Ludwig, on muscle current, 
109 ; on summation tones, 160. 

Hering, reference to, 13, 119; colour 
theory of, 127. 

Herschel, Sir John, reference to, 128. 

Heintz, physicist, 10. 

Hertz, Heinrich, reference to, 190, 
215, 217, 219. 

Hertz, Heinrich, Helmholtz on, 285 ; 
reference to, 243, 249. 

Hildebrand, crest of Helmholtz by, 

Hoffman, reference to, 20. 

Horopter, Helmholtz on the, 172 ; 

true form of, 179. 
Horopter, the, 260. 
Humboldt, Alexander von, reference 

tO, 21, 25. 

Hunter, John, reference to, 12. 
Huygens, reference to, 114, 239. 
Hydrodynamics, 194. 

ICE, 222. 

Infant, human, experience gained by, 

Italy, King of, reference to, 280. 

JACOBI, reference to, 43 ; on potential 

energy, 243. 

Jaeger, Von, reference to, 82. 
Jones, Bence, reference to, 91. 
Jones, Wharton, reference to, 77. 
Joule, on dynamical equivalent of heat, 

49, 51 ; reference to, 91. 

KANT, philosophy of, 253 ; on dynamics, 
237 ; on nature of judgments, 254 ; 
doctrine of space, 260 ; on the beauti 
ful, 268. 

Karsten, Gustav, physicist, 10. 

Kelvin, Lord, on thermodynamics, 52 ; 
friendship with Helmholtz, 92 ; on 
phase, 150 ; reference to, 165 ; on 
electricity, 211 ; on ice, 222 ; on dis- 
sipation of energy, 193 ; on theory of 
constitution of matter, 196, 198 ; on 
Faraday, 206 ; on rotational move- 
ments of ether, 253. 

Kinetic, potential, 247. 

Kirchhoff, reference to, 10, 43, 107, 184 

Klangfarbe, 143. 

Klerker, De, reference to, 230. 

Knots, Professor Tait on, 200. 

Koenigsberger, Leo, reference to, 236 

Konig, Arthur, reference to, 126. 

Konigsberg, 112. 

Konigsberg, University of, 58, 89. 

Kronecker, Hugo, reference to, 90. 

Kussmaul, reference to, 78. 

LAGRANGE, reference to, 195, 243. 
La Hire, reference to, 78. 
Lamarckian, principle of adaptation. 


Langenbeck, Max, reference to, 97. 
Laplace, mathematician, reference to, 

Lectures by Helmholtz, 274. 
Lectures, Helmholtz on, 276. 
Leeuwenhoek, reference to, 26 
Leibnitz, reference to, 40, 44 ; on 

dynamics, 46, 52, 230, 237, 243, 252, 


Linnaeus, reference to, 19. 
Liebig, reference to, 2r, 22, 28. 
Light, theory of, 114, 116. 
Lissajous, reference to, 166. 
Listing, schematic eye of, 102, 178. 
Lobatschewsky, reference to, 266. 



Locomotion, animal, Helmholtz on, 

Locke, John, on heat, 46 ; philosophy 

of, 251, 257. 
Lokman, fables of, 3. 
L6tze, reference to, 250. 
Levering, reference to, 199. 
Ludwig, Carl, reference to, n ; 

letter from Helmholtz to, 90. 

MAGNUS, Gustav, physicist, 10, 22 ; 
influence of teaching of, 22 ; death 
of, 184 ; lecture by Helmholtz on, 275. 

Marey, E.J., reference to, in. 

Maskeleyne, reference to, 70. 

Matteucci, reference to, 65; induced 
contraction, 65, 104. 

Maximilian, King of Bavaria, refer- 
ence to, 149. 

Maxwell, Clerk, reference to, 41, 122, 
185, 199, 207, 249, 264 ; on colour, 
112, 117; on dynamics, 48; on 
electro-dynamics, 213 ; on electro- 
magnetic waves, 216 j on Faraday, 
205 ; verse on mathematicians, 190. 

Maupertuis, reference to, 235. 

Mayer, Robert, reference to, 23, 48, 
54, 242. 

Medal, ophthalmological, presented to 
Helmholtz, 84. 

Medicine, lecture by Helmholtz on 
thought in, 277. 

Mellom, reference to, 118. 

Membrana tympani, action of, 133. 

Mendelssohn's ' Midsummer Night's 
Dream' music, 134, 284. 

Mery, reference to, 78. 

Meteorology, Helmholtz on, 232. 

Microscope, Helmholtz on, 232. 

Mirror, use of in physical experiment, 

Mitscherlich, reference to, 21, 22, 28. 

Mohl, Anna von, reference to, 187. 

Monads, Leibnitz's system of, 253. 

Montgolfier, on heat, 47. 

Montpellier, mathematicians of, 61. 

Muller, Johannes, anatomist, 10, 23 ; on 
eye, 24, 119, 129, 141, 152, 173, 178, 
25, 275; influence of, n ; specific 
energy of nerves, 13 ; on rate of 
nervous impulse, 65, 184. 

Mursinna, Surgeon-General, 8. 

Muscle, current, 105. 

Music, 134. 

Musicians, indifference to investiga- 
tion, 137. 

Myograph, 36. 

NEEF, interrupter of, 37. 
Nerve cells, discovery regarding, 15. 
Nerves, specific energy of, 13. 
Nervous impulse, rate of, 59. 
Negative variation, 107. 

Newton, reference to, 19, 44, 52, 44, 
45, 114, 117, 146 ; on the aether, 199 ; 
on action at a distance, 203, 242, 238, 

Neumann, F. C., reference to, 22, 204, 

Neumann, C., reference to, 205, 214. 

Nobili, reference to, 104. 

OHM, reference to, 22, 144, 145, 148. 

Ophthalmoiogical Congress at Heidel- 
berg, 84. 

Ophthalmometer, the, 92, 98. 

Ophthalmoscope, invention of, 71 ; 
theory of, 80. 

Optic nerves, course of fibres in, 174. 

Optics, Helmholtz on physical, 225. 

Organ pipes, Helmholtz on theory of, 

PAINTING, Helmholtz's ideas as to, 271. 

Paionios, reference to, 86. 

Pallas, reference to, 74. 

Partial tones, 147, 148. 

Penn, William, i. 

Phase, can the ear perceive, 148. 

Phidias, reference to, 85. 

Physical Society of Berlin, reference 

to, 41. 

Physico- Technical Institute, 185. 
Physiology, considered as a science, 

20 ; methods of, 29. 
Piotrowski, G. von, reference to, 202. 
Poggendorff, reference to, 22, 43, 227. 
Pouillet, reference to, 60, 62, 64. 
Praxiteles, reference to, 86. 
Prevost, reference to, 76. 
Principle of least action, 244. 
Pseudo-spherical surfaces, 263. 
Psycho-physical investigations, 70. 
Purkinje, images of, 95. 
Pythagoras, reference to, 148. 

QUINCKE, physicist, 10. 

RANKINE, Macquorne, reference to, 91. 

Rayleigh, Lord, on phase, 150, 189. 

Reed pipes, 167. 

Rekoss, reference to, 89. 

Reimer, G. E., reference to, 41. 

Reiss, reference to, 43. 

Rendu, reference to, 221. 

Resonators, 146. 

Reute, on ophthalmoscope, 78. 

Reymond, Du Bois, early friendship 
with Helmholtz, 10, 24, 35, 43, 60 ; 
on animal electricity, 65, 94, 104 ; 
physical theory of as to muscle cur- 
rent, 106, 184, 257, 284. 

Riemann, reference to, 139, 205, 214 ; 
notions as to space, 264. 

Riess, reference to, 22. 

Ritter, electrical experiments of, 20. 

Root, E., reference to, 210. 


Rowland, H. A., reference to, 210. 
Roux, Le, reference to, 229. 
Royal Institution of Great Britain, 32, 

Rucker, reference to, 207. 
Rudolphi, reference to, 76. 
Rumford, Count, reference to, 32, 47. 

Thorax, Helmholtz on movements of, 

Tidal actions, 221. 
Tone, analysis of, 104. 
Tones, combination, 159. 
Tones, compound nature of, 147. 
Tongue pipes, 161. 
Xyndall, reference to, u, 221, 273. 

SABINE, General, reference to, 91. 
Saccharomycetes, 26. 
Saccule, 138. 

UTRICLE, 138. 

Schelling, reference to, 20, 268 ; on art 
and science, 272. 
Schleiden, botanist, reference to, 12. 
Schlemm, canal of, 100. 
Schopenhauer, reference to, 268. 
Schroeder, reference to, 29. 
Schwann, reference to, 12 ; on fermen- 

VARIATION, negative, 107. 
Velten, Olga von, 58. 
Vibration microscope, 166. 
Violin, Helmholtz on strings of, 165. 
Virchow, early friend of Helmholtz, 10. 
Viscous fluids, 196. 
Vision, conditions of, 92 ; laws of, with 
one and with two eyes, 173. 

Scotch Highlands, reference to, 92. 
Seebeck, on thermo-electricity, 20. 
Seguin, on heat, 47. 
Semi-circular canals, 142. 

Volkmann, reference to, 284. 
Volta, reference to, 31. 
Voltaire, reference to, 32, 236. 
Vortex motion, 194. 

Sensations of tone, work on, 89, 131. 
Sharpey, physiologist, reference to, 14. 
Siemens, Werner, electrician, 10, 185, 
1 86. 

Vortex rings, 197. 
Vortices, nature of, 197. 
Vowel tones, 162. 
Vulpian, physiologist, reference to, 14. 

Smaasen, reference to, 107. 
Somerville, reference to, 47. 

WAGNER, reference to, 134 ; head of, 

Sound, physiological effect of, 133. 
Sound shadows, 166. 
Space, of various dimensions, 262, 265. 
Spencer, Herbert, reference to, 257. 
Spinoza, reference to, 252. 

Waterspouts, Helmholtz on, 223. 
Wave forms, 143. 
Weber, Wilhelm, reference to, 22; law 
of electrical attraction, 204, 207, 214, 

Stahl, reference to, 39. 
Steinway, Messrs, reference to, 167. 
Stokes, Sir G. G., reference to, gr, 


Weber, Ernst & Heinrich, 23, 153. 
Weber, C., on electrical irritation of 

195 ; on vortex motion, 197. 
Students, Helmholtz on judgment of, 

the eye, 100. 
Wheatstone, reference to, 91 ; stereo- 

Summation tones, TOO. 

Wiedemann, reference to, n, 22, 24, 

Sweden, King of, reference to, 280. 
Sylvester, Joseph, reference to, 190. 
Syren, polyphonic, of Helmholtz, 140. 

76, 191. 
William I., Emperor, reference to, 279. 
William II., Emperor, reference to, 

TAIT, reference to Prof. P. G., 44, 

YEAST, studies in, 27. 

45, 47, 200. 
Talbot, Fox, reference to, 228. 
Teachers, Helmholtz on, 276. 

Young, Thomas, reference to, 36, 122, 
123, 124, 152 ; compared with Helm- 
holtz, 287 ; on accommodation, 96 ; 

Telephone, Helmholtz on the, 167. 

on lens, 100 ; on light, 114; theory 

Telestereoscope of Helmholtz, 180. 

of colour, 117 ; use of rotating 

Temperature, influence of, on fermen- 

cylinder, 62 ; Helmholtz, theory of 

tation, 28. 

colour, 125. 

Thomson, Allen, reference to, 14. 

Thomson, James, reference to, 222. 
Thomson, Sir William, reference to, 

ZEHEXDER, Von, reference to, 84. 
Zeller, Eduard, reference to, 267. 

(see Kelvin, Lord). 

Zinn, zonule of, 101. 


2 99 

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